Calabi-Yau differential operator database v.3.0

1

New Number: 2.8 | AESZ: 63 | Superseeker: 684 195638820 | Hash: 06c1a4c0aa33f5051126908a9898430d

Degree: 2

$\theta^4-2^{2} 3 x(6\theta+1)(6\theta+5)(11\theta^2+11\theta+3)-2^{4} 3^{2} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 180, 263340, 600359760, 1674535082220, ...
--> OEIS
Normalized instanton numbers (n₀=1): 684, 253314, 195638820, 225040578570, 319342448936304, ... ; Common denominator:...

Discriminant

$1-4752z-186624z^2$

No data for singularities

Note:

Hadamard product D*b

	Gopakumar-Vafa invariants
g=0	3420, 1266570, 978194100, 1125202892850, 1596712244681520, 2593390973297156910, 4623712594996202607060, 8826751501399749729515490,...
g=1	1, -611, -3437965, 524537945, 45789504955348, 237013737984797903, 922140400732269341707, 3194302059028418771226413,...
g=2	,...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-310\)	\(62\)	\(5\)	\(6\)

2

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	,...

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

3

New Number: 4.44 | AESZ: 232 | Superseeker: 379/5 1364199/5 | Hash: 8d5ff690c87757ed51a092dee764eede

Degree: 4

$5^{2} \theta^4-5 x\left(2617\theta^4+4658\theta^3+3379\theta^2+1050\theta+120\right)+2^{6} 3 x^{2}\left(673\theta^4-4871\theta^3-10282\theta^2-5410\theta-860\right)+2^{10} 3^{2} x^{3}\left(955\theta^4+4320\theta^3+3477\theta^2+1020\theta+100\right)-2^{17} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 24, 3960, 974400, 292030200, ...
--> OEIS
Normalized instanton numbers (n₀=1): 379/5, 3346, 1364199/5, 177727432/5, 5658116533, ... ; Common denominator:...

Discriminant

$-(27z+1)(512z-1)(-5+96z)^2$

Local exponents

$-\frac{ 1}{ 27}$ $0$ $\frac{ 1}{ 512}$ $\frac{ 5}{ 96}$ $\infty$
$0$ $0$ $0$ $0$ $\frac{ 1}{ 3}$
$1$ $0$ $1$ $1$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $3$ $\frac{ 1}{ 2}$
$2$ $0$ $2$ $4$ $\frac{ 2}{ 3}$

\(-\frac{ 1}{ 27}\)	\(0\)	\(\frac{ 1}{ 512}\)	\(\frac{ 5}{ 96}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 3}\)
\(1\)	\(0\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)
\(1\)	\(0\)	\(1\)	\(3\)	\(\frac{ 1}{ 2}\)
\(2\)	\(0\)	\(2\)	\(4\)	\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-120\)	\(52\)	\(10\)	\(6\)

4

New Number: 5.101 | AESZ: 348 | Superseeker: -52 -44772 | Hash: 8759f016475d17d0fc88f4b98a374d3f

Degree: 5

$\theta^4+2^{2} x\left(70\theta^4+194\theta^3+145\theta^2+48\theta+6\right)-2^{4} 3 x^{2}\left(141\theta^4-858\theta^3-2111\theta^2-1192\theta-206\right)-2^{8} 3^{2} x^{3}\left(18\theta^4-324\theta^3-2364\theta^2-1953\theta-403\right)-2^{10} 3^{4} x^{4}(3\theta+1)(3\theta+2)(42\theta^2+258\theta+223)+2^{14} 3^{6} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, -24, 2160, -309120, 54608400, ...
--> OEIS
Normalized instanton numbers (n₀=1): -52, 461/2, -44772, 3546761/2, -178670332, ... ; Common denominator:...

Discriminant

$(746496z^3+17280z^2+352z+1)(-1+36z)^2$

Local exponents

≈$-0.009925-0.017537I$ ≈$-0.009925+0.017537I$ ≈$-0.003299$ $0$ $\frac{ 1}{ 36}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 3}$
$1$ $1$ $1$ $0$ $1$ $\frac{ 2}{ 3}$
$1$ $1$ $1$ $0$ $3$ $\frac{ 4}{ 3}$
$2$ $2$ $2$ $0$ $4$ $\frac{ 5}{ 3}$

≈\(-0.009925-0.017537I\)	≈\(-0.009925+0.017537I\)	≈\(-0.003299\)	\(0\)	\(\frac{ 1}{ 36}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 3}\)
\(1\)	\(1\)	\(1\)	\(0\)	\(1\)	\(\frac{ 2}{ 3}\)
\(1\)	\(1\)	\(1\)	\(0\)	\(3\)	\(\frac{ 4}{ 3}\)
\(2\)	\(2\)	\(2\)	\(0\)	\(4\)	\(\frac{ 5}{ 3}\)

Note:

This is operator "5.101" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-114\)	\(40\)	\(16\)	\(6\)

5

New Number: 5.14 | AESZ: 116 | Superseeker: 64 23360 | Hash: 0b366ad8c78b6697205c5a7fff270f5b

Degree: 5

$\theta^4-2^{5} x\left(10\theta^4+26\theta^3+20\theta^2+7\theta+1\right)+2^{8} x^{2}\left(52\theta^4+472\theta^3+832\theta^2+492\theta+103\right)+2^{16} x^{3}\left(14\theta^4+12\theta^3-96\theta^2-105\theta-29\right)-2^{18} x^{4}(2\theta+1)(56\theta^3+468\theta^2+646\theta+249)-2^{24} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 32, 2448, 273920, 38525200, ...
--> OEIS
Normalized instanton numbers (n₀=1): 64, 12, 23360, 654490, 53956288, ... ; Common denominator:...

Discriminant

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

Local exponents

$-\frac{ 1}{ 32}$ $0$ $\frac{ 1}{ 256}$ $\frac{ 1}{ 64}$ $\infty$
$0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $\frac{ 1}{ 2}$ $\frac{ 3}{ 4}$
$3$ $0$ $1$ $\frac{ 1}{ 2}$ $\frac{ 5}{ 4}$
$4$ $0$ $2$ $1$ $\frac{ 3}{ 2}$

\(-\frac{ 1}{ 32}\)	\(0\)	\(\frac{ 1}{ 256}\)	\(\frac{ 1}{ 64}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 1}{ 2}\)	\(\frac{ 3}{ 4}\)
\(3\)	\(0\)	\(1\)	\(\frac{ 1}{ 2}\)	\(\frac{ 5}{ 4}\)
\(4\)	\(0\)	\(2\)	\(1\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.14" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(40\)	\(40\)	\(16\)	\(6\)

6

New Number: 5.32 | AESZ: 215 | Superseeker: 220/3 89212 | Hash: ced61f5675491a3c4446c0e55e7bc36b

Degree: 5

$3^{2} \theta^4-2^{2} 3 x\left(268\theta^4+632\theta^3+463\theta^2+147\theta+18\right)-2^{7} x^{2}\left(448\theta^4-1616\theta^3-4280\theta^2-2418\theta-441\right)+2^{12} x^{3}\left(416\theta^4+2016\theta^3+756\theta^2-288\theta-135\right)+2^{19} x^{4}(8\theta^2-28\theta-33)(2\theta+1)^2-2^{24} x^{5}(2\theta+1)^2(2\theta+3)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 24, 2664, 470400, 102047400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 220/3, 3538/3, 89212, 7484350, 2459418080/3, ... ; Common denominator:...

Discriminant

$-(16z-1)(4096z^2-384z+1)(3+64z)^2$

Local exponents

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

\(-\frac{ 3}{ 64}\)	\(0\)	\(\frac{ 3}{ 64}-\frac{ 1}{ 32}\sqrt{ 2}\)	\(\frac{ 1}{ 16}\)	\(\frac{ 3}{ 64}+\frac{ 1}{ 32}\sqrt{ 2}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)
\(3\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 3}{ 2}\)
\(4\)	\(0\)	\(2\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.32" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-60\)	\(48\)	\(12\)	\(6\)

7

New Number: 5.83 | AESZ: 316 | Superseeker: 852/11 1678156/11 | Hash: b8201d587a016cc013e2477aadb5c1ff

Degree: 5

$11^{2} \theta^4-2^{2} 3 11 x\left(364\theta^4+824\theta^3+599\theta^2+187\theta+22\right)-2^{5} x^{2}\left(62164\theta^4+84496\theta^3+12499\theta^2-6402\theta-1584\right)-2^{4} 3 x^{3}\left(484016\theta^4+474144\theta^3+366952\theta^2+161832\theta+27027\right)-2^{11} 3^{2} x^{4}(964\theta^2+1360\theta+669)(2\theta+1)^2-2^{16} 3^{4} x^{5}(2\theta+1)^2(2\theta+3)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 24, 3240, 675600, 171901800, ...
--> OEIS
Normalized instanton numbers (n₀=1): 852/11, 21572/11, 1678156/11, 15912512, 22956446184/11, ... ; Common denominator:...

Discriminant

$-(2304z^3+1664z^2+432z-1)(11+192z)^2$

Local exponents

≈$-0.362258-0.240689I$ ≈$-0.362258+0.240689I$ $-\frac{ 11}{ 192}$ $0$ ≈$0.002294$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $1$ $0$ $1$ $\frac{ 1}{ 2}$
$1$ $1$ $3$ $0$ $1$ $\frac{ 3}{ 2}$
$2$ $2$ $4$ $0$ $2$ $\frac{ 3}{ 2}$

≈\(-0.362258-0.240689I\)	≈\(-0.362258+0.240689I\)	\(-\frac{ 11}{ 192}\)	\(0\)	≈\(0.002294\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(1\)	\(0\)	\(1\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(3\)	\(0\)	\(1\)	\(\frac{ 3}{ 2}\)
\(2\)	\(2\)	\(4\)	\(0\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.83" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-88\)	\(50\)	\(11\)	\(6\)

8

New Number: 5.86 | AESZ: 320 | Superseeker: 741/11 138745 | Hash: d19e7569ce62abdd5393977835e411a9

Degree: 5

$11^{2} \theta^4-11 x\left(4843\theta^4+8918\theta^3+6505\theta^2+2046\theta+242\right)+2^{2} x^{2}\left(312184\theta^4+343456\theta^3-23371\theta^2-73942\theta-14883\right)-2^{4} x^{3}\left(511972\theta^4+256344\theta^3+144969\theta^2+78639\theta+15642\right)+2^{11} x^{4}(2\theta+1)(1964\theta^3+3078\theta^2+1853\theta+419)-2^{18} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 22, 2850, 568300, 138119170, ...
--> OEIS
Normalized instanton numbers (n₀=1): 741/11, 22232/11, 138745, 157326644/11, 19999995398/11, ... ; Common denominator:...

Discriminant

$-(z-1)(64z^2-416z+1)(-11+128z)^2$

Local exponents

$0$ $\frac{ 13}{ 4}-\frac{ 15}{ 8}\sqrt{ 3}$ $\frac{ 11}{ 128}$ $1$ $\frac{ 13}{ 4}+\frac{ 15}{ 8}\sqrt{ 3}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $1$ $1$ $1$
$0$ $1$ $3$ $1$ $1$ $1$
$0$ $2$ $4$ $2$ $2$ $\frac{ 3}{ 2}$

\(0\)	\(\frac{ 13}{ 4}-\frac{ 15}{ 8}\sqrt{ 3}\)	\(\frac{ 11}{ 128}\)	\(1\)	\(\frac{ 13}{ 4}+\frac{ 15}{ 8}\sqrt{ 3}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(3\)	\(1\)	\(1\)	\(1\)
\(0\)	\(2\)	\(4\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.86" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-276\)	\(6\)	\(33\)	\(6\)

9

New Number: 5.91 | AESZ: 331 | Superseeker: 112 186800 | Hash: a30093d8c1ab2f66122cef8935b79efb

Degree: 5

$\theta^4+2^{4} x\left(18\theta^4-48\theta^3-33\theta^2-9\theta-1\right)-2^{9} x^{2}\left(86\theta^4+512\theta^3+125\theta^2+45\theta+10\right)-2^{14} x^{3}\left(1138\theta^4+2040\theta^3+1883\theta^2+879\theta+157\right)-2^{19} 7 x^{4}(2\theta+1)(186\theta^3+375\theta^2+317\theta+100)-2^{27} 7^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 16, 1488, 183040, 27611920, ...
--> OEIS
Normalized instanton numbers (n₀=1): 112, -2242, 186800, -11675813, 1250599376, ... ; Common denominator:...

Discriminant

$-(32z+1)(256z-1)(64z+1)(1+224z)^2$

Local exponents

$-\frac{ 1}{ 32}$ $-\frac{ 1}{ 64}$ $-\frac{ 1}{ 224}$ $0$ $\frac{ 1}{ 256}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $1$ $0$ $1$ $1$
$1$ $1$ $3$ $0$ $1$ $1$
$2$ $2$ $4$ $0$ $2$ $\frac{ 3}{ 2}$

\(-\frac{ 1}{ 32}\)	\(-\frac{ 1}{ 64}\)	\(-\frac{ 1}{ 224}\)	\(0\)	\(\frac{ 1}{ 256}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(1\)	\(0\)	\(1\)	\(1\)
\(1\)	\(1\)	\(3\)	\(0\)	\(1\)	\(1\)
\(2\)	\(2\)	\(4\)	\(0\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.91" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(68\)	\(40\)	\(16\)	\(6\)

10

New Number: 8.30 | AESZ: 314 | Superseeker: 229/4 297111/4 | Hash: 893692ba7eb3effcbc0c3b48d405456a

Degree: 8

$2^{4} \theta^4-2^{2} x\left(1282\theta^4+2618\theta^3+1909\theta^2+600\theta+72\right)-3^{2} x^{2}\left(9503\theta^4+26810\theta^3+31755\theta^2+15944\theta+2936\right)+3^{4} x^{3}\left(15627\theta^4-18288\theta^3-91412\theta^2-53256\theta-9688\right)+2 3^{6} x^{4}\left(15106\theta^4+20300\theta^3-20421\theta^2-23443\theta-5907\right)-2^{2} 3^{8} x^{5}\left(2072\theta^4-18256\theta^3-2563\theta^2+4626\theta+1495\right)-2^{2} 3^{10} x^{6}\left(6204\theta^4+360\theta^3-281\theta^2+1017\theta+434\right)-2^{5} 3^{12} x^{7}(2\theta+1)(100\theta^3+162\theta^2+95\theta+21)+2^{8} 3^{14} x^{8}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 18, 1926, 310860, 61060230, ...
--> OEIS
Normalized instanton numbers (n₀=1): 229/4, 1293, 297111/4, 6150238, 2540085295/4, ... ; Common denominator:...

Discriminant

$(z-1)(11664z^3+3888z^2+324z-1)(-4-9z+648z^2)^2$

Local exponents

≈$-0.168156-0.022431I$ ≈$-0.168156+0.022431I$ $\frac{ 1}{ 144}-\frac{ 1}{ 144}\sqrt{ 129}$ $0$ $\frac{ 1}{ 18}2^(\frac{ 1}{ 3})+\frac{ 1}{ 36}2^(\frac{ 2}{ 3})-\frac{ 1}{ 9}$ $\frac{ 1}{ 144}+\frac{ 1}{ 144}\sqrt{ 129}$ $1$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $1$ $0$ $1$ $1$ $1$ $1$
$1$ $1$ $3$ $0$ $1$ $3$ $1$ $1$
$2$ $2$ $4$ $0$ $2$ $4$ $2$ $\frac{ 3}{ 2}$

≈\(-0.168156-0.022431I\)	≈\(-0.168156+0.022431I\)	\(\frac{ 1}{ 144}-\frac{ 1}{ 144}\sqrt{ 129}\)	\(0\)	\(\frac{ 1}{ 18}2^(\frac{ 1}{ 3})+\frac{ 1}{ 36}2^(\frac{ 2}{ 3})-\frac{ 1}{ 9}\)	\(\frac{ 1}{ 144}+\frac{ 1}{ 144}\sqrt{ 129}\)	\(1\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(1\)
\(1\)	\(1\)	\(3\)	\(0\)	\(1\)	\(3\)	\(1\)	\(1\)
\(2\)	\(2\)	\(4\)	\(0\)	\(2\)	\(4\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "8.30" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-204\)	\(0\)	\(36\)	\(6\)

11

New Number: 8.32 | AESZ: 317 | Superseeker: 69/4 14365/12 | Hash: cda8cce31025f51636125bea67a820d1

Degree: 8

$2^{4} \theta^4-2^{2} 3 x\left(162\theta^4+414\theta^3+335\theta^2+128\theta+20\right)+3^{3} x^{2}\left(1219\theta^4+10906\theta^3+18963\theta^2+11824\theta+2708\right)+3^{5} 5 x^{3}\left(922\theta^4+162\theta^3-6403\theta^2-6576\theta-1964\right)-3^{7} x^{4}\left(10358\theta^4+58054\theta^3+62251\theta^2+29672\theta+4907\right)-3^{9} 5 x^{5}\left(1519\theta^4-1262\theta^3+1371\theta^2+4264\theta+1802\right)+2 3^{11} 5 x^{6}\left(1727\theta^4+3702\theta^3+3085\theta^2+882\theta+17\right)-3^{13} 5^{2} x^{7}\left(239\theta^4+460\theta^3+314\theta^2+84\theta+6\right)-3^{16} 5^{2} x^{8}\left((\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 15, 459, 19545, 1019259, ...
--> OEIS
Normalized instanton numbers (n₀=1): 69/4, -30, 14365/12, 3015/2, 1376205/4, ... ; Common denominator:...

Discriminant

$-(27z-1)(243z^3+2214z^2-117z+1)(-4-45z+405z^2)^2$

Local exponents

≈$-9.163702$ $\frac{ 1}{ 18}-\frac{ 1}{ 90}\sqrt{ 105}$ $0$ ≈$0.010727$ $\frac{ 1}{ 27}$ ≈$0.041864$ $\frac{ 1}{ 18}+\frac{ 1}{ 90}\sqrt{ 105}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $1$
$1$ $1$ $0$ $1$ $1$ $1$ $1$ $1$
$1$ $3$ $0$ $1$ $1$ $1$ $3$ $1$
$2$ $4$ $0$ $2$ $2$ $2$ $4$ $1$

≈\(-9.163702\)	\(\frac{ 1}{ 18}-\frac{ 1}{ 90}\sqrt{ 105}\)	\(0\)	≈\(0.010727\)	\(\frac{ 1}{ 27}\)	≈\(0.041864\)	\(\frac{ 1}{ 18}+\frac{ 1}{ 90}\sqrt{ 105}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(1\)	\(3\)	\(0\)	\(1\)	\(1\)	\(1\)	\(3\)	\(1\)
\(2\)	\(4\)	\(0\)	\(2\)	\(2\)	\(2\)	\(4\)	\(1\)

Note:

This operator has a second MUM-point at infininty corresponding to operator 8.31

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-88\)	\(50\)	\(11\)	\(6\)

12

New Number: 1.4 | AESZ: 4 | Superseeker: 117 713814 | Hash: 1f2a9672b7cdc68eae658b2304b40dbd

Degree: 1

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 36, 8100, 2822400, 1200622500, ...
--> OEIS
Normalized instanton numbers (n₀=1): 117, 5868, 713814, 126605376, 27754210287, ... ; Common denominator:...

Discriminant

$1-729z$

Local exponents

$0$ $\frac{ 1}{ 729}$ $\infty$
$0$ $0$ $\frac{ 1}{ 3}$
$0$ $1$ $\frac{ 1}{ 3}$
$0$ $1$ $\frac{ 2}{ 3}$
$0$ $2$ $\frac{ 2}{ 3}$

\(0\)	\(\frac{ 1}{ 729}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 1}{ 3}\)
\(0\)	\(1\)	\(\frac{ 1}{ 3}\)
\(0\)	\(1\)	\(\frac{ 2}{ 3}\)
\(0\)	\(2\)	\(\frac{ 2}{ 3}\)

Note:

A-incarnation: X(3,3) in P^5.

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-144\)	\(54\)	\(9\)	\(6\)

13

New Number: 1.6 | AESZ: 6 | Superseeker: 160 1956896 | Hash: 483b4ca5270ed3bfca9243827b62064e

Degree: 1

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 48, 15120, 7392000, 4414410000, ...
--> OEIS
Normalized instanton numbers (n₀=1): 160, 11536, 1956896, 485487816, 148865410272, ... ; Common denominator:...

Discriminant

$1-1024z$

Local exponents

$0$ $\frac{ 1}{ 1024}$ $\infty$
$0$ $0$ $\frac{ 1}{ 4}$
$0$ $1$ $\frac{ 1}{ 2}$
$0$ $1$ $\frac{ 1}{ 2}$
$0$ $2$ $\frac{ 3}{ 4}$

\(0\)	\(\frac{ 1}{ 1024}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(0\)	\(1\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(\frac{ 1}{ 2}\)
\(0\)	\(2\)	\(\frac{ 3}{ 4}\)

Note:

A-incarnation of $X(2,4)$ in $P^5$.

\(-\frac{ 18778337}{ 12500000}I\)	\(\frac{ 41}{ 12}\)	\(1\)	\(1\)
\(-\frac{ 31}{ 12}\)	\(-\frac{ 5}{ 2}\)	\(-1\)	\(0\)
\(0\)	\(5\)	\(0\)	\(0\)
\(-5\)	\(0\)	\(0\)	\(0\)

Calabi-Yau differential operator database v.3

Summary

Discriminant

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

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

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:

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)