Calabi-Yau differential operator database v.3.0

1

New Number: 2.1 | AESZ: 45 | Superseeker: 12 3204 | Hash: cdf289f6febf84eb577a238542a57457

Degree: 2

$\theta^4-2^{2} x(2\theta+1)^2(7\theta^2+7\theta+2)-2^{7} x^{2}(2\theta+1)^2(2\theta+3)^2$

Coefficients of the holomorphic solution: 1, 8, 360, 22400, 1695400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 12, 163, 3204, 107582, 4203360, ... ; Common denominator:...

Discriminant

$-(16z+1)(128z-1)$

Local exponents

$-\frac{ 1}{ 16}$ $0$ $\frac{ 1}{ 128}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $\frac{ 3}{ 2}$
$2$ $0$ $2$ $\frac{ 3}{ 2}$

\(-\frac{ 1}{ 16}\)	\(0\)	\(\frac{ 1}{ 128}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 1}{ 2}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 3}{ 2}\)
\(2\)	\(0\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

Hadamard product $A \ast a$, where $A$ is (:case 2.1.1)

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-120\)	\(72\)	\(24\)	\(10\)

2

New Number: 2.52 | AESZ: 16 | Superseeker: 4 644/3 | Hash: 05af0662662bfbec63e3186c4f363313

Degree: 2

$\theta^4-2^{2} x(2\theta+1)^2(5\theta^2+5\theta+2)+2^{8} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 168, 5120, 190120, ...
--> OEIS
Normalized instanton numbers (n₀=1): 4, 20, 644/3, 3072, 52512, ... ; Common denominator:...

Discriminant

$(64z-1)(16z-1)$

Local exponents

$0$ $\frac{ 1}{ 64}$ $\frac{ 1}{ 16}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $1$
$0$ $1$ $1$ $1$
$0$ $2$ $2$ $\frac{ 3}{ 2}$

\(0\)	\(\frac{ 1}{ 64}\)	\(\frac{ 1}{ 16}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)
\(0\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

Hadamard product $I \ast \alpha$
A-Incarnation: diagonal subfamily of 1,1,1,1-intersection in $P^1 \times P^1 \times P^1 \times \P^1$
B-Incarnations:
Fibre products: 62211- x 632--1, S62211

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-128\)	\(96\)	\(48\)	\(16\)

3

New Number: 2.55 | AESZ: 42 | Superseeker: 8 1000 | Hash: c389d3bc0e31801bc4b7b3e186702bc9

Degree: 2

$\theta^4-2^{3} x(2\theta+1)^2(3\theta^2+3\theta+1)+2^{6} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 240, 10880, 597520, ...
--> OEIS
Normalized instanton numbers (n₀=1): 8, 63, 1000, 44369/2, 606168, ... ; Common denominator:...

Discriminant

$1-96z+256z^2$

Local exponents

$0$ $\frac{ 3}{ 16}-\frac{ 1}{ 8}\sqrt{ 2}$ $\frac{ 3}{ 16}+\frac{ 1}{ 8}\sqrt{ 2}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $1$
$0$ $1$ $1$ $1$
$0$ $2$ $2$ $\frac{ 3}{ 2}$

\(0\)	\(\frac{ 3}{ 16}-\frac{ 1}{ 8}\sqrt{ 2}\)	\(\frac{ 3}{ 16}+\frac{ 1}{ 8}\sqrt{ 2}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)
\(0\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

Hadamard product $I \ast \epsilon$

	Gopakumar-Vafa invariants
g=0	256, 2016, 32000, 709904, 19397376, 604985440, 20693162240, 757512952944,...
g=1	0, 0, 0, -8, 1024, 1220032, 162833408, 14777331408,...
g=2	,...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-116\)	\(80\)	\(32\)	\(12\)

4

New Number: 2.61 | AESZ: 26 | Superseeker: 10 1724 | Hash: f3fc09474973b19b8bdb783e3322eb65

Degree: 2

$\theta^4-2 x(2\theta+1)^2(13\theta^2+13\theta+4)-2^{2} 3 x^{2}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 288, 15200, 968800, ...
--> OEIS
Normalized instanton numbers (n₀=1): 10, 191/2, 1724, 45680, 1478214, ... ; Common denominator:...

Discriminant

$-(4z+1)(108z-1)$

Local exponents

$-\frac{ 1}{ 4}$ $0$ $\frac{ 1}{ 108}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $\frac{ 2}{ 3}$
$1$ $0$ $1$ $\frac{ 4}{ 3}$
$2$ $0$ $2$ $\frac{ 3}{ 2}$

\(-\frac{ 1}{ 4}\)	\(0\)	\(\frac{ 1}{ 108}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 2}{ 3}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 4}{ 3}\)
\(2\)	\(0\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

A-incarnation: $X(1,1,1,1,2) \subset Grass(2,6)$

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-116\)	\(76\)	\(28\)	\(11\)

5

New Number: 2.69 | AESZ: 205 | Superseeker: 1 5 | Hash: 4fb2e7002e630237d0458c3985cd6a18

Degree: 2

$\theta^4-x\left(59\theta^4+118\theta^3+105\theta^2+46\theta+8\right)+2^{5} 3 x^{2}(\theta+1)^2(3\theta+2)(3\theta+4)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 120, 2240, 46840, ...
--> OEIS
Normalized instanton numbers (n₀=1): 1, 7/4, 5, 24, 759/5, ... ; Common denominator:...

Discriminant

$(32z-1)(27z-1)$

Local exponents

$0$ $\frac{ 1}{ 32}$ $\frac{ 1}{ 27}$ $\infty$
$0$ $0$ $0$ $\frac{ 2}{ 3}$
$0$ $1$ $1$ $1$
$0$ $1$ $1$ $1$
$0$ $2$ $2$ $\frac{ 4}{ 3}$

\(0\)	\(\frac{ 1}{ 32}\)	\(\frac{ 1}{ 27}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 2}{ 3}\)
\(0\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)
\(0\)	\(2\)	\(2\)	\(\frac{ 4}{ 3}\)

Note:

This is operator "2.69" from ...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-128\)	\(160\)	\(160\)	\(40\)

6

New Number: 3.31 | AESZ: | Superseeker: 4 284 | Hash: 660b0951ad934fc17fda7eb9b1750649

Degree: 3

$\theta^4-2^{2} x(2\theta+1)^2(5\theta^2+5\theta+2)+2^{5} x^{2}(2\theta+1)(2\theta+3)(7\theta^2+14\theta+8)-2^{4} 11 x^{3}(2\theta+1)(2\theta+3)^2(2\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 168, 5360, 210280, ...
--> OEIS
Normalized instanton numbers (n₀=1): 4, 27, 284, 4368, 80968, ... ; Common denominator:...

Discriminant

$1-80z+896z^2-2816z^3$

No data for singularities

Note:

This is operator "3.31" from ...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

7

New Number: 3.9 | AESZ: ~101 | Superseeker: 13 2650 | Hash: a6878d847acf199583e8168a33967174

Degree: 3

$\theta^4-x\left(113\theta^4+226\theta^3+173\theta^2+60\theta+8\right)-2^{3} x^{2}(\theta+1)^2(119\theta^2+238\theta+92)-2^{2} 11^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 336, 19880, 1420720, ...
--> OEIS
Normalized instanton numbers (n₀=1): 13, 128, 2650, 79400, 2921395, ... ; Common denominator:...

Discriminant

$-(121z-1)(4z+1)^2$

Local exponents

$-\frac{ 1}{ 4}$ $0$ $\frac{ 1}{ 121}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$\frac{ 1}{ 2}$ $0$ $1$ $1$
$\frac{ 1}{ 2}$ $0$ $1$ $2$
$1$ $0$ $2$ $\frac{ 5}{ 2}$

\(-\frac{ 1}{ 4}\)	\(0\)	\(\frac{ 1}{ 121}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(\frac{ 1}{ 2}\)	\(0\)	\(1\)	\(1\)
\(\frac{ 1}{ 2}\)	\(0\)	\(1\)	\(2\)
\(1\)	\(0\)	\(2\)	\(\frac{ 5}{ 2}\)

Note:

Operator equivalent to $AESZ 101=$b \ast b$.

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-100\)	\(70\)	\(25\)	\(10\)

8

New Number: 4.33 | AESZ: 55 | Superseeker: 76/3 144196/3 | Hash: 7e88cd5b7dc1c51022b66ac6f009218f

Degree: 4

$3^{2} \theta^4-2^{2} 3 x\left(208\theta^4+224\theta^3+163\theta^2+51\theta+6\right)+2^{9} x^{2}\left(32\theta^4-928\theta^3-1606\theta^2-837\theta-141\right)+2^{16} x^{3}\left(144\theta^4+576\theta^3+467\theta^2+144\theta+15\right)-2^{24} x^{4}\left((2\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 936, 108800, 16748200, ...
--> OEIS
Normalized instanton numbers (n₀=1): 76/3, 3476/3, 144196/3, 3563196, 309069600, ... ; Common denominator:...

Discriminant

$-(64z+1)(256z-1)(-3+128z)^2$

Local exponents

$-\frac{ 1}{ 64}$ $0$ $\frac{ 1}{ 256}$ $\frac{ 3}{ 128}$ $\infty$
$0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $1$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $3$ $\frac{ 1}{ 2}$
$2$ $0$ $2$ $4$ $\frac{ 1}{ 2}$

\(-\frac{ 1}{ 64}\)	\(0\)	\(\frac{ 1}{ 256}\)	\(\frac{ 3}{ 128}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(0\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)
\(1\)	\(0\)	\(1\)	\(3\)	\(\frac{ 1}{ 2}\)
\(2\)	\(0\)	\(2\)	\(4\)	\(\frac{ 1}{ 2}\)

Note:

Sporadic operator. There is a second MUM-point
hiding at infinity, corresponding to Operator 4.56

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-88\)	\(48\)	\(12\)	\(6\)

9

New Number: 4.42 | AESZ: 222 | Superseeker: 69/5 29081/5 | Hash: aad7a72e711c9c463396d319e0bf7603

Degree: 4

$5^{2} \theta^4-5 x\left(407\theta^4+1198\theta^3+909\theta^2+310\theta+40\right)-2^{7} x^{2}\left(2103\theta^4+6999\theta^3+8358\theta^2+4050\theta+680\right)-2^{12} x^{3}\left(1387\theta^4+3840\theta^3+3081\theta^2+960\theta+100\right)-2^{21} x^{4}\left((2\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 504, 36800, 3518200, ...
--> OEIS
Normalized instanton numbers (n₀=1): 69/5, 1383/4, 29081/5, 346080, 72023607/5, ... ; Common denominator:...

Discriminant

$-(8192z^2+107z-1)(5+64z)^2$

Local exponents

$-\frac{ 5}{ 64}$ $-\frac{ 107}{ 16384}-\frac{ 51}{ 16384}\sqrt{ 17}$ $0$ $s_1$ $s_2$ $-\frac{ 107}{ 16384}+\frac{ 51}{ 16384}\sqrt{ 17}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $0$ $1$ $1$ $1$ $\frac{ 1}{ 2}$
$3$ $1$ $0$ $1$ $1$ $1$ $\frac{ 1}{ 2}$
$4$ $2$ $0$ $2$ $2$ $2$ $\frac{ 1}{ 2}$

\(-\frac{ 5}{ 64}\)	\(-\frac{ 107}{ 16384}-\frac{ 51}{ 16384}\sqrt{ 17}\)	\(0\)	\(s_1\)	\(s_2\)	\(-\frac{ 107}{ 16384}+\frac{ 51}{ 16384}\sqrt{ 17}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)
\(3\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)
\(4\)	\(2\)	\(0\)	\(2\)	\(2\)	\(2\)	\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ225/4.43

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-128\)	\(68\)	\(20\)	\(9\)

10

New Number: 5.107 | AESZ: 364 | Superseeker: 11/5 71/5 | Hash: c5b4bc60bc9d39ea420bd49fad182557

Degree: 5

$5^{2} \theta^4-5 x\left(553\theta^4+722\theta^3+611\theta^2+250\theta+40\right)+2^{6} x^{2}\left(1914\theta^4+4722\theta^3+5519\theta^2+3010\theta+610\right)-2^{12} x^{3}\left(685\theta^4+2400\theta^3+3466\theta^2+2220\theta+500\right)+2^{19} x^{4}(2\theta+1)(30\theta^3+105\theta^2+122\theta+46)-2^{25} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 120, 2240, 50680, ...
--> OEIS
Normalized instanton numbers (n₀=1): 11/5, -8/5, 71/5, 738, 26841/5, ... ; Common denominator:...

Discriminant

$-(32768z^3-2560z^2+85z-1)(-5+64z)^2$

Local exponents

$0$ ≈$0.023029$ ≈$0.027548-0.023797I$ ≈$0.027548+0.023797I$ $\frac{ 5}{ 64}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $1$ $1$ $1$
$0$ $1$ $1$ $1$ $3$ $1$
$0$ $2$ $2$ $2$ $4$ $\frac{ 3}{ 2}$

\(0\)	≈\(0.023029\)	≈\(0.027548-0.023797I\)	≈\(0.027548+0.023797I\)	\(\frac{ 5}{ 64}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)	\(3\)	\(1\)
\(0\)	\(2\)	\(2\)	\(2\)	\(4\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.107" from ...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

11

New Number: 5.10 | AESZ: 59 | Superseeker: 30/7 124 | Hash: f47563daeb0f7328bd675f13cfb84a55

Degree: 5

$7^{2} \theta^4-2 7 x\left(257\theta^4+520\theta^3+435\theta^2+175\theta+28\right)+2^{2} x^{2}\left(13497\theta^4+55536\theta^3+81222\theta^2+50337\theta+11396\right)-2^{3} x^{3}\left(17201\theta^4+114996\theta^3+248466\theta^2+202629\theta+55412\right)-2^{4} x^{4}\left(5762\theta^4+29668\theta^3+48150\theta^2+31741\theta+7412\right)-2^{5} 3 x^{5}(4\theta+5)(3\theta+2)(3\theta+4)(4\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 144, 3680, 114400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 30/7, 129/14, 124, 72129/56, 130434/7, ... ; Common denominator:...

Discriminant

$-(4z-1)(16z-1)(54z-1)(7+2z)^2$

Local exponents

$-\frac{ 7}{ 2}$ $0$ $\frac{ 1}{ 54}$ $\frac{ 1}{ 16}$ $\frac{ 1}{ 4}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 2}{ 3}$
$1$ $0$ $1$ $1$ $1$ $\frac{ 3}{ 4}$
$3$ $0$ $1$ $1$ $1$ $\frac{ 5}{ 4}$
$4$ $0$ $2$ $2$ $2$ $\frac{ 4}{ 3}$

\(-\frac{ 7}{ 2}\)	\(0\)	\(\frac{ 1}{ 54}\)	\(\frac{ 1}{ 16}\)	\(\frac{ 1}{ 4}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 2}{ 3}\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 3}{ 4}\)
\(3\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 5}{ 4}\)
\(4\)	\(0\)	\(2\)	\(2\)	\(2\)	\(\frac{ 4}{ 3}\)

Note:

This is operator "5.10" from ...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-78\)	\(92\)	\(56\)	\(17\)

12

New Number: 5.110 | AESZ: 377 | Superseeker: 32/3 6752/3 | Hash: 4b8e1b4341fae957e1766a0071de5ba5

Degree: 5

$3^{2} \theta^4-2^{3} 3 x\left(61\theta^4+74\theta^3+58\theta^2+21\theta+3\right)+2^{4} x^{2}\left(3883\theta^4+5356\theta^3+3451\theta^2+1278\theta+228\right)-2^{7} x^{3}\left(8067\theta^4+13410\theta^3+12875\theta^2+6336\theta+1236\right)+2^{14} x^{4}\left(413\theta^4+1069\theta^3+1206\theta^2+658\theta+140\right)-2^{19} 3 x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 264, 13760, 873640, ...
--> OEIS
Normalized instanton numbers (n₀=1): 32/3, 731/6, 6752/3, 355219/6, 5936896/3, ... ; Common denominator:...

Discriminant

$-(4z-1)(108z-1)(8z-1)(-3+64z)^2$

Local exponents

$0$ $\frac{ 1}{ 108}$ $\frac{ 3}{ 64}$ $\frac{ 1}{ 8}$ $\frac{ 1}{ 4}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 2}{ 3}$
$0$ $1$ $1$ $1$ $1$ $1$
$0$ $1$ $3$ $1$ $1$ $1$
$0$ $2$ $4$ $2$ $2$ $\frac{ 4}{ 3}$

Note:

This is operator "5.110" from ...

13

New Number: 5.24 | AESZ: 195 | Superseeker: 285/29 40626/29 | Hash: 49a600431b3e9aaa9d9d6947f8df7d2b

Degree: 5

$29^{2} \theta^4-29 x\left(3026\theta^4+5848\theta^3+4577\theta^2+1653\theta+232\right)+x^{2}\left(5568+57768\theta+239159\theta^2+424220\theta^3+258647\theta^4\right)-x^{3}\left(76560+336864\theta+581647\theta^2+532614\theta^3+272743\theta^4\right)+2^{2} 17 x^{4}\left(1922\theta^4+6193\theta^3+8121\theta^2+4894\theta+1112\right)-2^{2} 3 17^{2} x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 264, 13040, 778840, ...
--> OEIS
Normalized instanton numbers (n₀=1): 285/29, 2362/29, 40626/29, 997476/29, 30096841/29, ... ; Common denominator:...

Discriminant

$-(27z^3-67z^2+102z-1)(-29+34z)^2$

Local exponents

$0$ ≈$0.009868$ $\frac{ 29}{ 34}$ ≈$1.235807-1.492036I$ ≈$1.235807+1.492036I$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 2}{ 3}$
$0$ $1$ $1$ $1$ $1$ $1$
$0$ $1$ $3$ $1$ $1$ $1$
$0$ $2$ $4$ $2$ $2$ $\frac{ 4}{ 3}$

Note:

This is operator "5.24" from ...

14

New Number: 5.39 | AESZ: 224 | Superseeker: 59/5 22503/5 | Hash: ba17e8cb074bba75e7a27206be530698

Degree: 5

$5^{2} \theta^4-5 x\left(1057\theta^4+1058\theta^3+819\theta^2+290\theta+40\right)+2^{5} x^{2}\left(10123\theta^4+11419\theta^3+5838\theta^2+1510\theta+180\right)-2^{8} x^{3}\left(30981\theta^4+46560\theta^3+48211\theta^2+25500\theta+5100\right)+2^{14} 11 x^{4}(2\theta+1)(234\theta^3+591\theta^2+581\theta+202)-2^{20} 11^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 312, 19520, 1475320, ...
--> OEIS
Normalized instanton numbers (n₀=1): 59/5, 186, 22503/5, 718052/5, 29091017/5, ... ; Common denominator:...

Discriminant

$-(128z-1)(128z^2-13z+1)(-5+176z)^2$

Local exponents

$0$ $\frac{ 1}{ 128}$ $\frac{ 5}{ 176}$ $\frac{ 13}{ 256}-\frac{ 7}{ 256}\sqrt{ 7}I$ $\frac{ 13}{ 256}+\frac{ 7}{ 256}\sqrt{ 7}I$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $1$ $1$ $1$
$0$ $1$ $3$ $1$ $1$ $1$
$0$ $2$ $4$ $2$ $2$ $\frac{ 3}{ 2}$

Note:

This is operator "5.39" from ...

15

New Number: 5.51 | AESZ: 250 | Superseeker: 308/23 70799/23 | Hash: 9c19794a84073d1c6dfd11c8a7c9a740

Degree: 5

$23^{2} \theta^4-23 x\left(3271\theta^4+5078\theta^3+3896\theta^2+1357\theta+184\right)+x^{2}\left(1357863\theta^4+999924\theta^3-787393\theta^2-850862\theta-205712\right)-2^{3} x^{3}\left(775799\theta^4-272481\theta^3-218821\theta^2+176709\theta+100234\right)-2^{4} 61 x^{4}\left(1005\theta^4-15654\theta^3-36317\theta^2-27938\theta-7304\right)-2^{9} 61^{2} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 324, 19304, 1388260, ...
--> OEIS
Normalized instanton numbers (n₀=1): 308/23, 3526/23, 70799/23, 2148684/23, 81402822/23, ... ; Common denominator:...

Discriminant

$-(512z^3+113z^2+121z-1)(-23+244z)^2$

Local exponents

≈$-0.114451-0.474453I$ ≈$-0.114451+0.474453I$ $0$ ≈$0.008199$ $\frac{ 23}{ 244}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 3}{ 4}$
$1$ $1$ $0$ $1$ $1$ $1$
$1$ $1$ $0$ $1$ $3$ $1$
$2$ $2$ $0$ $2$ $4$ $\frac{ 5}{ 4}$

Note:

This is operator "5.51" from ...

16

New Number: 5.6 | AESZ: 23 | Superseeker: 4/3 44/3 | Hash: 65760d446ba9c3da587ce5bd9912745e

Degree: 5

$3^{2} \theta^4-2^{2} 3 x\left(64\theta^4+80\theta^3+73\theta^2+33\theta+6\right)+2^{7} x^{2}\left(194\theta^4+440\theta^3+527\theta^2+315\theta+75\right)-2^{12} x^{3}\left(94\theta^4+288\theta^3+397\theta^2+261\theta+66\right)+2^{17} x^{4}\left(22\theta^4+80\theta^3+117\theta^2+77\theta+19\right)-2^{23} x^{5}\left((\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 104, 1664, 30376, ...
--> OEIS
Normalized instanton numbers (n₀=1): 4/3, 13/3, 44/3, 278/3, 2336/3, ... ; Common denominator:...

Discriminant

$-(-1+32z)(16z-1)^2(32z-3)^2$

Local exponents

$0$ $\frac{ 1}{ 32}$ $\frac{ 1}{ 16}$ $\frac{ 3}{ 32}$ $\infty$
$0$ $0$ $0$ $0$ $1$
$0$ $1$ $\frac{ 1}{ 2}$ $1$ $1$
$0$ $1$ $\frac{ 1}{ 2}$ $3$ $1$
$0$ $2$ $1$ $4$ $1$

Note:

There is a second MUM-point at infinity,corresponding to Operator AESZ 56/5.9
A-Incarnation: (2,0),(2.0),(0,2),(0,2),(1,1).intersection in $P^4 \times P^4$

17

New Number: 5.73 | AESZ: 293 | Superseeker: 20 13188 | Hash: f19eeaee48396d15d7cf7be47d7d48a7

Degree: 5

$\theta^4-2^{2} x\left(54\theta^4+66\theta^3+49\theta^2+16\theta+2\right)+2^{4} x^{2}\left(417\theta^4-306\theta^3-1219\theta^2-776\theta-154\right)+2^{8} x^{3}\left(166\theta^4+1920\theta^3+1589\theta^2+432\theta+23\right)-2^{12} 7 x^{4}(2\theta+1)(38\theta^3+45\theta^2+12\theta-2)-2^{14} 7^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 528, 45440, 4763920, ...
--> OEIS
Normalized instanton numbers (n₀=1): 20, 867/2, 13188, 609734, 35512476, ... ; Common denominator:...

Discriminant

$-(16z+1)(256z^2+176z-1)(-1+28z)^2$

Local exponents

$-\frac{ 11}{ 32}-\frac{ 5}{ 32}\sqrt{ 5}$ $-\frac{ 1}{ 16}$ $0$ $-\frac{ 11}{ 32}+\frac{ 5}{ 32}\sqrt{ 5}$ $\frac{ 1}{ 28}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $0$ $1$ $1$ $1$
$1$ $1$ $0$ $1$ $3$ $1$
$2$ $2$ $0$ $2$ $4$ $\frac{ 3}{ 2}$

Note:

This is operator "5.73" from ...

18

New Number: 5.88 | AESZ: 324 | Superseeker: 148/11 44108/11 | Hash: 7f84d776cf00ff399b20865542185f87

Degree: 5

$11^{2} \theta^4-2^{2} 11 x\left(432\theta^4+624\theta^3+477\theta^2+165\theta+22\right)+2^{5} x^{2}\left(12944\theta^4+4736\theta^3-15491\theta^2-12914\theta-2860\right)-2^{4} 5 x^{3}\left(10688\theta^4-114048\theta^3-159132\theta^2-83028\theta-15455\right)-2^{11} 5^{2} x^{4}(2\theta+1)(4\theta+3)(76\theta^2+189\theta+125)+2^{14} 5^{3} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 360, 23120, 1796200, ...
--> OEIS
Normalized instanton numbers (n₀=1): 148/11, 2044/11, 44108/11, 1459636/11, 60212712/11, ... ; Common denominator:...

Discriminant

$(5120z^3-512z^2-128z+1)(-11+160z)^2$

Local exponents

≈$-0.120643$ $0$ ≈$0.007599$ $\frac{ 11}{ 160}$ ≈$0.213044$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $1$ $1$ $\frac{ 3}{ 4}$
$1$ $0$ $1$ $3$ $1$ $\frac{ 5}{ 4}$
$2$ $0$ $2$ $4$ $2$ $\frac{ 3}{ 2}$

Note:

This is operator "5.88" from ...

19

New Number: 5.96 | AESZ: 339 | Superseeker: 12 28 | Hash: 41593acc689cf76c174442db98218947

Degree: 5

$\theta^4-2^{2} x\left(10\theta^4+50\theta^3+39\theta^2+14\theta+2\right)+2^{4} x^{2}\left(177\theta^4+1158\theta^3+2007\theta^2+1158\theta+230\right)+2^{8} x^{3}\left(539\theta^4+1344\theta^3-300\theta^2-1068\theta-340\right)+2^{10} 5 x^{4}(2\theta+1)(4\theta^3-642\theta^2-1002\theta-385)-2^{13} 3 5^{2} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 0, -6400, -249200, ...
--> OEIS
Normalized instanton numbers (n₀=1): 12, -339/2, 28, 27639/2, 634692, ... ; Common denominator:...

Discriminant

$-(55296z^3-5632z^2+80z-1)(1+20z)^2$

Local exponents

$-\frac{ 1}{ 20}$ $0$ ≈$0.007072-0.012497I$ ≈$0.007072+0.012497I$ ≈$0.087707$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $1$ $1$ $\frac{ 2}{ 3}$
$3$ $0$ $1$ $1$ $1$ $\frac{ 4}{ 3}$
$4$ $0$ $2$ $2$ $2$ $\frac{ 3}{ 2}$

Note:

This is operator "5.96" from ...

20

New Number: 7.11 | AESZ: | Superseeker: -8 -3784/3 | Hash: cb1bf6566f9c1a0dbfe98fb55f81944c

Degree: 7

$\theta^4+2^{2} x\left(23\theta^4-34\theta^3-30\theta^2-13\theta-2\right)+2^{5} x^{2}\left(177\theta^4+108\theta^3+577\theta^2+518\theta+116\right)+2^{10} x^{3}\left(355\theta^4+960\theta^3+1178\theta^2+139\theta-44\right)+2^{15} x^{4}\left(451\theta^4+1228\theta^3+997\theta^2+489\theta+103\right)+2^{20} x^{5}\left(285\theta^4+720\theta^3+766\theta^2+410\theta+83\right)+2^{26} x^{6}(2\theta+1)(20\theta^3+50\theta^2+49\theta+17)+2^{31} x^{7}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, -120, -4480, 55720, ...
--> OEIS
Normalized instanton numbers (n₀=1): -8, 43/2, -3784/3, 51036, -1659840, ... ; Common denominator:...

Discriminant

$(8z+1)(32768z^3+3072z^2-12z+1)(32z+1)^3$

Local exponents

$-\frac{ 1}{ 8}$ ≈$-0.100423$ $-\frac{ 1}{ 32}$ $0$ ≈$0.003336-0.01711I$ ≈$0.003336+0.01711I$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $2$ $0$ $1$ $1$ $1$
$1$ $1$ $3$ $0$ $1$ $1$ $1$
$2$ $2$ $5$ $0$ $2$ $2$ $\frac{ 3}{ 2}$

Note:

This is operator "7.11" from ...

21

New Number: 8.28 | AESZ: 303 | Superseeker: 151/13 26293/13 | Hash: e081c85684dd16a72eeaf5a1b139b912

Degree: 8

$13^{2} \theta^4-13 x\left(1505\theta^4+2746\theta^3+2127\theta^2+754\theta+104\right)+2^{2} x^{2}\left(22961\theta^4-2086\theta^3-55741\theta^2-41574\theta-9256\right)+2^{5} x^{3}\left(7524\theta^4+28098\theta^3+16131\theta^2+2691\theta-52\right)-2^{7} x^{4}\left(7241\theta^4+6214\theta^3+17522\theta^2+15423\theta+4146\right)-2^{8} x^{5}\left(6087\theta^4+1806\theta^3-3905\theta^2-3796\theta-1036\right)+2^{10} x^{6}\left(553\theta^4+4062\theta^3+4405\theta^2+1752\theta+220\right)+2^{14} x^{7}\left(82\theta^4+230\theta^3+275\theta^2+160\theta+37\right)+2^{18} x^{8}\left((\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 292, 15776, 1030036, ...
--> OEIS
Normalized instanton numbers (n₀=1): 151/13, 1436/13, 26293/13, 719465/13, 24184128/13, ... ; Common denominator:...

Discriminant

$(z-1)(64z^3+304z^2+108z-1)(-13+44z+64z^2)^2$

Local exponents

≈$-4.362346$ $-\frac{ 11}{ 32}-\frac{ 1}{ 32}\sqrt{ 329}$ ≈$-0.396684$ $0$ ≈$0.009029$ $-\frac{ 11}{ 32}+\frac{ 1}{ 32}\sqrt{ 329}$ $1$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $1$
$1$ $1$ $1$ $0$ $1$ $1$ $1$ $1$
$1$ $3$ $1$ $0$ $1$ $3$ $1$ $1$
$2$ $4$ $2$ $0$ $2$ $4$ $2$ $1$

Note:

This operator has a second MUM-point at infinity corresponding to operator 8.29

22

New Number: 8.3 | AESZ: 105 | Superseeker: 8 -104 | Hash: 7b27135451cf2016217211c633b7ab83

Degree: 8

$\theta^4-2^{2} x(3\theta^2+3\theta+1)(7\theta^2+7\theta+2)+2^{5} 3 x^{2}\left(15\theta^4+28\theta^3+39\theta^2+22\theta+4\right)-2^{10} x^{3}\left(21\theta^4-126\theta^3-386\theta^2-291\theta-76\right)+2^{14} x^{4}\left(37\theta^4+74\theta^3+50\theta^2+13\theta+6\right)+2^{18} x^{5}\left(21\theta^4+210\theta^3+118\theta^2-19\theta-24\right)+2^{21} 3 x^{6}\left(15\theta^4+32\theta^3+45\theta^2+32\theta+8\right)+2^{26} x^{7}(3\theta^2+3\theta+1)(7\theta^2+7\theta+2)+2^{32} x^{8}\left((\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 200, 6272, 233896, ...
--> OEIS
Normalized instanton numbers (n₀=1): 8, 71/2, -104, 4202, 50112, ... ; Common denominator:...

Discriminant

$(8z+1)(64z-1)(4z+1)(32z-1)(1+256z^2)^2$

Local exponents

$-\frac{ 1}{ 4}$ $-\frac{ 1}{ 8}$ $0-\frac{ 1}{ 16}I$ $0$ $0+\frac{ 1}{ 16}I$ $\frac{ 1}{ 64}$ $\frac{ 1}{ 32}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $1$
$1$ $1$ $1$ $0$ $1$ $1$ $1$ $1$
$1$ $1$ $3$ $0$ $3$ $1$ $1$ $1$
$2$ $2$ $4$ $0$ $4$ $2$ $2$ $1$

Note:

Hadamard product $a \ast d$. This operator has a second MUM-point at infinity with the same instanton numbers.
It can be reduced to an operator of degree 4 with a single MUM-point defined over
$Q(\sqrt{-1})$.

23

New Number: 8.41 | AESZ: | Superseeker: 16 7568/3 | Hash: 051d7068f49d14c45c3c3369d63d56b5

Degree: 8

$3^{2} \theta^4-2^{2} 3^{2} x\left(23\theta^4+58\theta^3+44\theta^2+15\theta+2\right)-2^{5} 3 x^{2}\left(254\theta^4+662\theta^3+623\theta^2+309\theta+66\right)-2^{8} 3 x^{3}\left(569\theta^4+1092\theta^3+602\theta^2+285\theta+78\right)-2^{11} x^{4}\left(2266\theta^4+4076\theta^3+2167\theta^2+537\theta+18\right)-2^{16} x^{5}\left(519\theta^4+798\theta^3+821\theta^2+391\theta+62\right)-2^{19} x^{6}\left(305\theta^4+558\theta^3+625\theta^2+360\theta+82\right)-2^{24} x^{7}\left(26\theta^4+70\theta^3+83\theta^2+48\theta+11\right)-2^{29} x^{8}\left((\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 328, 18944, 1324456, ...
--> OEIS
Normalized instanton numbers (n₀=1): 16, 751/6, 7568/3, 229516/3, 8099456/3, ... ; Common denominator:...

Discriminant

$-(4z+1)(2048z^3+768z^2+112z-1)(3+24z+256z^2)^2$

Local exponents

$-\frac{ 1}{ 4}$ ≈$-0.191715-0.145483I$ ≈$-0.191715+0.145483I$ $-\frac{ 3}{ 64}-\frac{ 1}{ 64}\sqrt{ 39}I$ $-\frac{ 3}{ 64}+\frac{ 1}{ 64}\sqrt{ 39}I$ $0$ ≈$0.00843$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $1$
$1$ $1$ $1$ $1$ $1$ $0$ $1$ $1$
$1$ $1$ $1$ $3$ $3$ $0$ $1$ $1$
$2$ $2$ $2$ $4$ $4$ $0$ $2$ $1$

Note:

This is operator "8.41" from ...

24

New Number: 8.43 | AESZ: | Superseeker: 66/7 8716/7 | Hash: 923554dba37f79c41bf0f67b875c36f7

Degree: 8

$7^{2} \theta^4-2 7 x\left(452\theta^4+640\theta^3+509\theta^2+189\theta+28\right)+2^{2} x^{2}\left(47156\theta^4+78224\theta^3+63963\theta^2+31010\theta+7000\right)-2^{5} x^{3}\left(77224\theta^4+150936\theta^3+155876\theta^2+86751\theta+19838\right)+2^{8} x^{4}\left(65988\theta^4+160584\theta^3+193653\theta^2+117501\theta+28198\right)-2^{12} x^{5}\left(15712\theta^4+46888\theta^3+63382\theta^2+41163\theta+10338\right)+2^{16} x^{6}\left(2088\theta^4+7272\theta^3+10589\theta^2+7140\theta+1828\right)-2^{22} x^{7}\left(36\theta^4+138\theta^3+206\theta^2+137\theta+34\right)+2^{26} x^{8}\left((\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 224, 10016, 547936, ...
--> OEIS
Normalized instanton numbers (n₀=1): 66/7, 573/7, 8716/7, 197852/7, 5617614/7, ... ; Common denominator:...

Discriminant

$(1-96z+256z^2)(4z-1)^2(128z^2-88z+7)^2$

Local exponents

$0$ $\frac{ 3}{ 16}-\frac{ 1}{ 8}\sqrt{ 2}$ $\frac{ 11}{ 32}-\frac{ 1}{ 32}\sqrt{ 65}$ $\frac{ 1}{ 4}$ $\frac{ 3}{ 16}+\frac{ 1}{ 8}\sqrt{ 2}$ $\frac{ 11}{ 32}+\frac{ 1}{ 32}\sqrt{ 65}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $1$
$0$ $1$ $1$ $\frac{ 1}{ 2}$ $1$ $1$ $1$
$0$ $1$ $3$ $\frac{ 1}{ 2}$ $1$ $3$ $1$
$0$ $2$ $4$ $1$ $2$ $4$ $1$

Note:

This is operator "8.43" from ...

25

New Number: 8.49 | AESZ: | Superseeker: 56/3 17704/3 | Hash: 4fa01cbee2fc74e3a62e00386e6fa1c0

Degree: 8

$3^{2} \theta^4-2^{2} 3 x\left(29\theta^4+178\theta^3+134\theta^2+45\theta+6\right)-2^{5} x^{2}\left(2233\theta^4+2536\theta^3+607\theta^2+132\theta+12\right)-2^{10} x^{3}\left(1274\theta^4+7425\theta^3+20002\theta^2+12717\theta+2670\right)+2^{13} x^{4}\left(2539\theta^4-36538\theta^3-52775\theta^2-31122\theta-6192\right)+2^{20} x^{5}\left(1617\theta^4+9771\theta^3+4484\theta^2-674\theta-556\right)+2^{25} x^{6}\left(1135\theta^4+4272\theta^3+3439\theta^2+858\theta+16\right)-2^{31} 3 x^{7}(2\theta+1)(110\theta^3+225\theta^2+184\theta+57)+2^{37} 3^{2} x^{8}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 264, 16640, 1130920, ...
--> OEIS
Normalized instanton numbers (n₀=1): 56/3, -83/6, 17704/3, -25024/3, 13408832/3, ... ; Common denominator:...

Discriminant

$(4z-1)(131072z^3+2048z^2+88z-1)(48z+1)^2(64z-3)^2$

Local exponents

$-\frac{ 1}{ 48}$ ≈$-0.01214-0.027095I$ ≈$-0.01214+0.027095I$ $0$ ≈$0.008655$ $\frac{ 3}{ 64}$ $\frac{ 1}{ 4}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $1$ $0$ $1$ $1$ $1$ $1$
$3$ $1$ $1$ $0$ $1$ $3$ $1$ $1$
$4$ $2$ $2$ $0$ $2$ $4$ $2$ $\frac{ 3}{ 2}$

Note:

This is operator "8.49" from ...

26

New Number: 8.68 | AESZ: | Superseeker: 6/17 33/17 | Hash: 0c0662f5b46ac6cb0bd298a63cf364c7

Degree: 8

$17^{2} \theta^4+17 x\theta(165\theta^3-114\theta^2-74\theta-17)-x^{2}\left(20619\theta^4+122880\theta^3+175353\theta^2+126480\theta+36992\right)-2 x^{3}\left(201857\theta^4+853944\theta^3+1437673\theta^2+1174122\theta+375972\right)-2^{2} x^{4}\left(571275\theta^4+2711616\theta^3+5301571\theta^2+4856674\theta+1694372\right)-2^{3} 3 x^{5}(\theta+1)(295815\theta^3+1523993\theta^2+2924668\theta+1983212)-2^{5} x^{6}(\theta+1)(\theta+2)(558823\theta^2+2951265\theta+4136951)-2^{7} 3 37 x^{7}(\theta+3)(\theta+2)(\theta+1)(2797\theta+9878)-2^{9} 3^{2} 7 37^{2} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 0, 8, 24, 288, ...
--> OEIS
Normalized instanton numbers (n₀=1): 6/17, 25/34, 33/17, 157/17, 577/17, ... ; Common denominator:...

Discriminant

$-(12z-1)(6z+1)(7z^2-z+1)(4z+1)^2(74z+17)^2$

Local exponents

$-\frac{ 1}{ 4}$ $-\frac{ 17}{ 74}$ $-\frac{ 1}{ 6}$ $0$ $\frac{ 1}{ 14}-\frac{ 3}{ 14}\sqrt{ 3}I$ $\frac{ 1}{ 14}+\frac{ 3}{ 14}\sqrt{ 3}I$ $\frac{ 1}{ 12}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $1$
$\frac{ 1}{ 2}$ $1$ $1$ $0$ $1$ $1$ $1$ $2$
$\frac{ 1}{ 2}$ $3$ $1$ $0$ $1$ $1$ $1$ $3$
$1$ $4$ $2$ $0$ $2$ $2$ $2$ $4$

Note:

This is operator "8.68" from ...

27

New Number: 8.69 | AESZ: | Superseeker: 4 52 | Hash: e303d10e77a367612be2fb706f37b895

Degree: 8

$\theta^4-2^{2} x\left(20\theta^4+34\theta^3+29\theta^2+12\theta+2\right)+2^{4} x^{2}\left(125\theta^4+362\theta^3+471\theta^2+284\theta+66\right)-2^{7} x^{3}\left(191\theta^4+606\theta^3+855\theta^2+588\theta+154\right)+2^{10} x^{4}\left(192\theta^4+552\theta^3+562\theta^2+268\theta+49\right)-2^{13} x^{5}\left(134\theta^4+380\theta^3+373\theta^2+124\theta+3\right)+2^{16} x^{6}\left(61\theta^4+150\theta^3+173\theta^2+93\theta+19\right)-2^{19} x^{7}\left(19\theta^4+50\theta^3+56\theta^2+31\theta+7\right)+2^{23} x^{8}\left((\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 128, 2816, 74896, ...
--> OEIS
Normalized instanton numbers (n₀=1): 4, 15/2, 52, 1563/2, 7276, ... ; Common denominator:...

Discriminant

$(16z-1)(8z-1)(64z^2-48z+1)(1-4z+32z^2)^2$

Local exponents

$0$ $\frac{ 3}{ 8}-\frac{ 1}{ 4}\sqrt{ 2}$ $\frac{ 1}{ 16}-\frac{ 1}{ 16}\sqrt{ 7}I$ $\frac{ 1}{ 16}$ $\frac{ 1}{ 16}+\frac{ 1}{ 16}\sqrt{ 7}I$ $\frac{ 1}{ 8}$ $\frac{ 3}{ 8}+\frac{ 1}{ 4}\sqrt{ 2}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $1$
$0$ $1$ $1$ $1$ $1$ $1$ $1$ $1$
$0$ $1$ $3$ $1$ $3$ $1$ $1$ $1$
$0$ $2$ $4$ $2$ $4$ $2$ $2$ $1$

Note:

This is operator "8.69" from ...

28

New Number: 8.77 | AESZ: | Superseeker: 91/5 25991/5 | Hash: fa37d863a8d0cc4b7a34e7d9b5e3a1a5

Degree: 8

$5^{2} \theta^4-5 x\left(693\theta^4+1242\theta^3+931\theta^2+310\theta+40\right)-2^{4} x^{2}\left(659\theta^4+9977\theta^3+17174\theta^2+10200\theta+2160\right)-2^{5} x^{3}\left(7235\theta^4-19374\theta^3-34715\theta^2-7290\theta+1560\right)-2^{8} x^{4}\left(14861\theta^4+40168\theta^3-70511\theta^2-88342\theta-26424\right)-2^{10} x^{5}\left(6973\theta^4+29386\theta^3+99859\theta^2+58446\theta+9864\right)-2^{14} x^{6}\left(6951\theta^4-25713\theta^3-34544\theta^2-14472\theta-1680\right)-2^{15} 11 x^{7}\left(2029\theta^4+5030\theta^3+5139\theta^2+2570\theta+520\right)+2^{18} 3 11^{2} x^{8}(\theta+1)^2(3\theta+2)(3\theta+4)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 408, 28160, 2360440, ...
--> OEIS
Normalized instanton numbers (n₀=1): 91/5, 1158/5, 25991/5, 192163, 42855113/5, ... ; Common denominator:...

Discriminant

$(z-1)(8z+1)(864z^2+136z-1)(5-24z+352z^2)^2$

Local exponents

$-\frac{ 17}{ 216}-\frac{ 7}{ 216}\sqrt{ 7}$ $-\frac{ 1}{ 8}$ $0$ $-\frac{ 17}{ 216}+\frac{ 7}{ 216}\sqrt{ 7}$ $\frac{ 3}{ 88}-\frac{ 1}{ 88}\sqrt{ 101}I$ $\frac{ 3}{ 88}+\frac{ 1}{ 88}\sqrt{ 101}I$ $1$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $\frac{ 2}{ 3}$
$1$ $1$ $0$ $1$ $1$ $1$ $1$ $1$
$1$ $1$ $0$ $1$ $3$ $3$ $1$ $1$
$2$ $2$ $0$ $2$ $4$ $4$ $2$ $\frac{ 4}{ 3}$

Note:

This is operator "8.77" from ...

29

New Number: 24.10 | AESZ: | Superseeker: 23/3 -11450/81 | Hash: 38f69d10efcf1cecb893b4ec6e7f935d

Degree: 24

\(3^{3} \theta^4-3^{2} x(12\theta^2+11\theta+3)(20\theta^2+21\theta+8)+3 x^{2}\left(19299\theta^4+78796\theta^3+109877\theta^2+63446\theta+14016\right)-x^{3}\left(15470\theta^4+866668\theta^3+2069017\theta^2+1671401\theta+536214\right)-x^{4}\left(1138248\theta^4+1706550\theta^3-2534918\theta^2-3025945\theta-915072\right)+x^{5}\left(28756154\theta^4+60366300\theta^3-109333109\theta^2-137943099\theta-45737664\right)+x^{6}\left(32843719\theta^4-191583028\theta^3+237130805\theta^2+463457074\theta+223186208\right)-x^{7}\left(917154124\theta^4-565053944\theta^3-97751313\theta^2+679349929\theta+398163454\right)+x^{8}\left(3589458339\theta^4-2727679080\theta^3-1302482752\theta^2+1396143960\theta+694946880\right)-2 x^{9}\left(1937917032\theta^4-3189394128\theta^3-5013912813\theta^2-2923204701\theta-506481748\right)-2 x^{10}\left(2325299271\theta^4+9545434500\theta^3+17001134089\theta^2+14158555322\theta+4243430976\right)+2 x^{11}\left(5245867146\theta^4+13216454796\theta^3+20436911015\theta^2+14552765547\theta+3114426494\right)-2^{3} x^{12}\left(36094918\theta^4-1955241496\theta^3-6780107635\theta^2-9739362200\theta-5187586578\right)-2 x^{13}\left(4132995702\theta^4+21853487820\theta^3+54264334273\theta^2+65679813131\theta+3068268959\right)+2 x^{14}\left(1091890963\theta^4-83664300\theta^3-11910268959\theta^2-27816528978\theta-19410718768\right)+2 x^{15}\left(1567811420\theta^4+11417192080\theta^3+33555079093\theta^2+46454705111\theta+24010188798\right)-x^{16}\left(1103983063\theta^4+1933621792\theta^3-9275189128\theta^2-33319252360\theta-27425598384\right)-3 x^{17}\left(235027408\theta^4+1942700472\theta^3+5394877285\theta^2+6482788569\theta+2730469456\right)+3^{3} x^{18}\left(10056633\theta^4+28880428\theta^3-33255815\theta^2-234311274\theta-218971008\right)+3^{2} x^{19}\left(13371098\theta^4+122671124\theta^3+358242019\theta^2+410729083\theta+154355754\right)-2^{2} 3^{3} x^{20}\left(299324\theta^4+476670\theta^3-1853764\theta^2-5444373\theta-3656884\right)-3^{4} x^{21}\left(170942\theta^4+1362148\theta^3+4194121\theta^2+5361887\theta+2399352\right)+3^{4} x^{22}\left(29459\theta^4+79820\theta^3-94487\theta^2-420110\theta-301056\right)+3^{6} 5 x^{23}(\theta+2)(404\theta^3+2048\theta^2+3577\theta+2149)+3^{8} 5^{2} x^{24}\left((\theta+2)^4\right)\)

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 115, 1604, 32881/6, ...
--> OEIS
Normalized instanton numbers (n₀=1): 23/3, -629/36, -11450/81, -525798481/248832, -33700238207857/2916000000, ... ; Common denominator:...

Discriminant

$27-2160z+2386179z^22+1472580z^23+164025z^24+32843719z^6-917154124z^7+3589458339z^8-3875834064z^9-4650598542z^10-1103983063z^16-705082224z^17+57897z^2-15470z^3-1138248z^4+28756154z^5+271529091z^18+10491734292z^11-288759344z^12-8265991404z^13+2183781926z^14+3135622840z^15+120339882z^19-32326992z^20-13846302z^21$

No data for singularities

Note:

This is operator "24.10" from ...

30

New Number: 24.13 | AESZ: | Superseeker: -112 -1046539024/273375 | Hash: 516bcee6a8de593c5564ec440efe3b8d

Degree: 24

\(5^{2} \theta^4-2^{2} 5 x\left(59\theta^4+309\theta^3+60\theta+10\right)-2^{4} x^{2}\left(1691\theta^4+968\theta^3-2159\theta^2-3710\theta-1280\right)+2^{6} x^{3}\left(5072\theta^4+6804\theta^3-10968\theta^2-19920\theta-6125\right)+2^{8} x^{4}\left(20906\theta^4+1456\theta^3+368\theta^2+98982\theta+52315\right)-2^{10} x^{5}\left(38226\theta^4+1368\theta^3-31034\theta^2+196580\theta+102479\right)-2^{12} x^{6}\left(80590\theta^4+85368\theta^3+572076\theta^2+153630\theta-36895\right)+2^{14} x^{7}\left(171070\theta^4-87304\theta^3+378218\theta^2+262804\theta+39177\right)+2^{16} x^{8}\left(1992\theta^4+1030728\theta^3+1426960\theta^2+1361234\theta+669383\right)-2^{18} x^{9}\left(393556\theta^4+370236\theta^3+491768\theta^2+168948\theta-44105\right)+2^{20} x^{10}\left(464128\theta^4-1479640\theta^3-3029898\theta^2-5078698\theta-2800421\right)+2^{22} x^{11}\left(144814\theta^4+2374096\theta^3-153374\theta^2+438540\theta+229919\right)-2^{24} x^{12}\left(676638\theta^4+1061016\theta^3-2384336\theta^2-6296046\theta-4366613\right)+2^{26} x^{13}\left(524030\theta^4-129368\theta^3-100270\theta^2-684012\theta-257057\right)+2^{28} x^{14}\left(26658\theta^4+904584\theta^3-1081360\theta^2-4536770\theta-3722999\right)-2^{30} x^{15}\left(303262\theta^4-173112\theta^3-869286\theta^2-2492316\theta-1729219\right)+2^{32} x^{16}\left(150991\theta^4+448664\theta^3+2076176\theta^2+3525718\theta+2153109\right)-2^{34} x^{17}\left(59541\theta^4+1414230\theta^3+5805485\theta^2+9562624\theta+5566627\right)+2^{36} x^{18}\left(105307\theta^4+1480128\theta^3+6044899\theta^2+10098756\theta+6006305\right)-2^{39} x^{19}\left(35483\theta^4+377170\theta^3+1606033\theta^2+2831774\theta+1765587\right)-2^{42} x^{20}\left(1755\theta^4+2910\theta^3-80552\theta^2-253489\theta-204789\right)+2^{44} x^{21}\left(5593\theta^4+49638\theta^3+148313\theta^2+187164\theta+85503\right)-2^{46} 3 x^{22}\left(375\theta^4+4228\theta^3+14881\theta^2+21402\theta+11011\right)-2^{49} 3^{2} x^{23}\left(21\theta^4+142\theta^3+375\theta^2+454\theta+211\right)+2^{52} 3^{3} x^{24}\left((\theta+2)^4\right)\)

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 124, 1722272/405, 369030281/2025, ...
--> OEIS
Normalized instanton numbers (n₀=1): -112, 11681/50, -1046539024/273375, 64922948419/4860000, -1775354639652176/2373046875, ... ; Common denominator:...

Discriminant

$(4z+1)(16z^2-4z-1)(16384z^6-2048z^5+768z^4-256z^3+288z^2+56z-1)(4z-1)^2(2048z^5-512z^4-832z^3+272z^2-68z+5)^2(12z+1)^3$

No data for singularities

Note:

This is operator "24.13" from ...

\(4+240\lambda\)	\(-\frac{ 3}{ 2}-120\lambda\)	\(\frac{ 5}{ 8}+50\lambda\)	\(-.159319280-30\lambda\)
\(10\)	\(-4\)	\(\frac{ 25}{ 12}\)	\(-\frac{ 5}{ 8}-50\lambda\)
\(24\)	\(-12\)	\(6\)	\(-\frac{ 3}{ 2}-120\lambda\)
\(48\)	\(-24\)	\(10\)	\(-2-240\lambda\)

\(5+512\lambda\)	\(-1.-.620290874I\)	\(\frac{ 1}{ 3}+\frac{ 128}{ 3}\lambda\)	\(-\frac{ 1}{ 7}7^{ \frac{ 5}{ 8})exp(-\frac{ 9}{ 4}}Zeta(5)^(\frac{ 1}{ 4})-\frac{ 64}{ 3}\lambda\)
\(16\)	\(-3\)	\(\frac{ 4}{ 3}\)	\(-\frac{ 1}{ 3}-\frac{ 128}{ 3}\lambda\)
\(48\)	\(-12\)	\(5\)	\(-1.-.620290874I\)
\(192\)	\(-48\)	\(16\)	\(-3-512\lambda\)

\(9.+5.059247438I\)	\(-\frac{ 8}{ 3}-348\lambda\)	\(.83333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333+.527004941I\)	\(-.133347276-58\lambda\)
\(30\)	\(-9\)	\(\frac{ 25}{ 8}\)	\(-.83333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-.527004941I\)
\(96\)	\(-32\)	\(11\)	\(-\frac{ 8}{ 3}-348\lambda\)
\(288+\frac{ 1}{ 1000000000}I\)	\(-96\)	\(30\)	\(-7.-5.059247438I\)

\(\frac{ 20}{ 3}+464\lambda\)	\(-\frac{ 17}{ 6}-232\lambda\)	\(1.0456349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349+.414911827I\)	\(-.241563519-.227532292I\)
\(\frac{ 62}{ 3}\)	\(-\frac{ 28}{ 3}\)	\(\frac{ 961}{ 252}\)	\(-1.0456349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349-.414911827I\)
\(56\)	\(-28\)	\(\frac{ 34}{ 3}\)	\(-\frac{ 17}{ 6}-232\lambda\)
\(112\)	\(-56\)	\(\frac{ 62}{ 3}\)	\(-\frac{ 14}{ 3}-464\lambda\)

\(3.333327178+1.235680918I\)	\(-.293785798-.155290034I\)	\(.97173439e-1+.52174089e-1I\)	\(-.12126753e-1-.18089273e-1I\)
\(13.327492354-.18865422e-1I\)	\(-.677351606+.3680160e-2I\)	\(.556724039+.2392839e-2I\)	\(-.96900942e-1-.51907518e-1I\)
\(39.969803488-.74697659e-1I\)	\(-5.030457990+.13317419e-1I\)	\(2.669647034+\frac{ 1}{ 243}IPi^{ \frac{ 1}{ 6}}Zeta(5)^7\)	\(-.290681436-.15554156171284634760705289672544080604534005037783375314861460957178841309823677581863979848866498740554156171284634760705289672544080604534005037783375314861460957178841309823677581863979848866498741I\)
\(319.859816505-.452770130I\)	\(-40.256438534+.88323845e-1I\)	\(13.361376945+.57428145e-1I\)	\(-1.325622606-1.245780435I\)

\(1\)	\(-1\)	\(\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 6}\)
\(0\)	\(1\)	\(-1\)	\(\frac{ 1}{ 2}\)
\(0\)	\(0\)	\(1\)	\(-1\)
\(0\)	\(0\)	\(0\)	\(1\)

\(1+120\lambda\)	\(0\)	\(15\lambda\)	\(.14090360e-1\)
\(3\)	\(1\)	\(\frac{ 3}{ 8}\)	\(-15\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(24\)	\(0\)	\(3\)	\(1-120\lambda\)

\(-120\lambda\)	\(7\)	\(1\)	\(1\)
\(-3\)	\(-12\)	\(-1\)	\(0\)
\(0\)	\(24\)	\(0\)	\(0\)
\(-24\)	\(0\)	\(0\)	\(0\)

\(1.+.620290874I\)	\(0\)	\(\frac{ 32}{ 3}\lambda\)	\(.8015849e-2\)
\(4\)	\(1\)	\(\frac{ 1}{ 3}\)	\(-\frac{ 32}{ 3}\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(48\)	\(0\)	\(4\)	\(1.-.620290874I\)

\(-\frac{ 310145437}{ 500000000}I\)	\(12\)	\(1\)	\(1\)
\(-4\)	\(-24\)	\(-1\)	\(0\)
\(0\)	\(48\)	\(0\)	\(0\)
\(-48\)	\(0\)	\(0\)	\(0\)

\(1+116\lambda\)	\(0\)	\(\frac{ 1}{ 343}I5^{ \frac{ 7}{ 9}}7^{ \frac{ 1}{ 3}}ln(2)^3\)	\(.9874994e-2\)
\(\frac{ 10}{ 3}\)	\(1\)	\(\frac{ 25}{ 72}\)	\(-\frac{ 1}{ 343}I5^{ \frac{ 7}{ 9}}7^{ \frac{ 1}{ 3}}ln(2)^3\)
\(0\)	\(0\)	\(1\)	\(0\)
\(32\)	\(0\)	\(\frac{ 10}{ 3}\)	\(1-116\lambda\)

\(-116\lambda\)	\(\frac{ 26}{ 3}\)	\(1\)	\(1\)
\(-\frac{ 10}{ 3}\)	\(-16\)	\(-1\)	\(0\)
\(0\)	\(32\)	\(0\)	\(0\)
\(-32\)	\(0\)	\(0\)	\(0\)

\(1+116\lambda\)	\(0\)	\(.63575199e-1I\)	\(\frac{ 79}{ 7000}\)
\(\frac{ 19}{ 6}\)	\(1\)	\(\frac{ 361}{ 1008}\)	\(-.63575199e-1I\)
\(0\)	\(0\)	\(1\)	\(0\)
\(28\)	\(0\)	\(\frac{ 19}{ 6}\)	\(1-116\lambda\)

\(-116\lambda\)	\(\frac{ 47}{ 6}\)	\(1\)	\(1\)
\(-\frac{ 19}{ 6}\)	\(-14\)	\(-1\)	\(0\)
\(0\)	\(28\)	\(0\)	\(0\)
\(-28\)	\(0\)	\(0\)	\(0\)

\(1.+.620290874I\)	\(0\)	\(\frac{ 16}{ 3}\lambda\)	\(.2404755e-2\)
\(\frac{ 20}{ 3}\)	\(1\)	\(\frac{ 5}{ 18}\)	\(-\frac{ 16}{ 3}\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(160\)	\(0\)	\(\frac{ 20}{ 3}\)	\(1.-.620290874I\)

\(-\frac{ 310145437}{ 500000000}I\)	\(\frac{ 100}{ 3}\)	\(1\)	\(1\)
\(-\frac{ 20}{ 3}\)	\(-80\)	\(-1\)	\(0\)
\(0\)	\(160\)	\(0\)	\(0\)
\(-160\)	\(0\)	\(0\)	\(0\)

Calabi-Yau differential operator database v.3

Summary

Discriminant

Local exponents

Note:

Explicit solution

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note: