Calabi-Yau differential operator database v.3.0

1

New Number: 2.11 | AESZ: 69 | Superseeker: 64 246848 | Hash: 729adc350de26d9415643078ed8d3867

Degree: 2

$\theta^4-2^{2} x(4\theta+1)(4\theta+3)(10\theta^2+10\theta+3)+2^{4} 3^{2} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 36, 6300, 1718640, 575675100, ...
--> OEIS
Normalized instanton numbers (n₀=1): 64, 2616, 246848, 32024824, 5160268864, ... ; Common denominator:...

Discriminant

$(576z-1)(64z-1)$

Local exponents

$0$ $\frac{ 1}{ 576}$ $\frac{ 1}{ 64}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$0$ $1$ $1$ $\frac{ 3}{ 4}$
$0$ $1$ $1$ $\frac{ 5}{ 4}$
$0$ $2$ $2$ $\frac{ 7}{ 4}$

\(0\)	\(\frac{ 1}{ 576}\)	\(\frac{ 1}{ 64}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 3}{ 4}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 5}{ 4}\)
\(0\)	\(2\)	\(2\)	\(\frac{ 7}{ 4}\)

Note:

Hadamard product $C\ast c$

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-224\)	\(72\)	\(12\)	\(8\)

2

New Number: 2.3 | AESZ: 68 | Superseeker: 52 220220 | Hash: 13a48045ff0a42a9fcfbdb710baf1997

Degree: 2

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 24, 4200, 1034880, 311711400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 52, 2814, 220220, 29135058, 4512922272, ... ; Common denominator:...

Discriminant

$-(64z+1)(512z-1)$

Local exponents

$-\frac{ 1}{ 64}$ $0$ $\frac{ 1}{ 512}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$1$ $0$ $1$ $\frac{ 3}{ 4}$
$1$ $0$ $1$ $\frac{ 5}{ 4}$
$2$ $0$ $2$ $\frac{ 7}{ 4}$

\(-\frac{ 1}{ 64}\)	\(0\)	\(\frac{ 1}{ 512}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 3}{ 4}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 5}{ 4}\)
\(2\)	\(0\)	\(2\)	\(\frac{ 7}{ 4}\)

Note:

C*a

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-228\)	\(72\)	\(12\)	\(8\)

3

New Number: 2.6 | AESZ: 24 | Superseeker: 36 41421 | Hash: 5e8f8f32b5e99693a2956e1240b9fdff

Degree: 2

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 18, 1710, 246960, 43347150, ...
--> OEIS
Normalized instanton numbers (n₀=1): 36, 837, 41421, 2992851, 266362506, ... ; Common denominator:...

Discriminant

$1-297z-729z^2$

Local exponents

$-\frac{ 11}{ 54}-\frac{ 5}{ 54}\sqrt{ 5}$ $0$ $-\frac{ 11}{ 54}+\frac{ 5}{ 54}\sqrt{ 5}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 3}$
$1$ $0$ $1$ $\frac{ 2}{ 3}$
$1$ $0$ $1$ $\frac{ 4}{ 3}$
$2$ $0$ $2$ $\frac{ 5}{ 3}$

\(-\frac{ 11}{ 54}-\frac{ 5}{ 54}\sqrt{ 5}\)	\(0\)	\(-\frac{ 11}{ 54}+\frac{ 5}{ 54}\sqrt{ 5}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 3}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 2}{ 3}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 4}{ 3}\)
\(2\)	\(0\)	\(2\)	\(\frac{ 5}{ 3}\)

Note:

Hadamard product B*b
Related to 7.19, 8.18
This operator corresponds to $(Grass(2,5)\vert 1,1,3)_{-150}$ from arXiv:0802.2908

	Gopakumar-Vafa invariants
g=0	540, 12555, 621315, 44892765, 3995437590, 406684089360, 45426958360155, 5432556927598425,...
g=1	0, 0, -1, 13095, 17230617, 6648808835, 1831575868830, 433375127634753,...
g=2	,...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-150\)	\(66\)	\(15\)	\(8\)

4

New Number: 4.45 | AESZ: 233 | Superseeker: 80 104976 | Hash: 03f67459f6d678669f766c99281b1e79

Degree: 4

$\theta^4-2^{4} x\left(83\theta^4+94\theta^3+71\theta^2+24\theta+3\right)+2^{11} 3 x^{2}\left(101\theta^4+191\theta^3+174\theta^2+71\theta+10\right)-2^{16} 3^{2} x^{3}\left(203\theta^4+432\theta^3+333\theta^2+102\theta+11\right)+2^{23} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 48, 9360, 2553600, 813027600, ...
--> OEIS
Normalized instanton numbers (n₀=1): 80, 2794, 104976, 5367454, 508265072, ... ; Common denominator:...

Discriminant

$(512z-1)(432z-1)(-1+192z)^2$

Local exponents

$0$ $\frac{ 1}{ 512}$ $\frac{ 1}{ 432}$ $\frac{ 1}{ 192}$ $\infty$
$0$ $0$ $0$ $0$ $\frac{ 1}{ 3}$
$0$ $1$ $1$ $1$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $3$ $\frac{ 1}{ 2}$
$0$ $2$ $2$ $4$ $\frac{ 2}{ 3}$

\(0\)	\(\frac{ 1}{ 512}\)	\(\frac{ 1}{ 432}\)	\(\frac{ 1}{ 192}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 3}\)
\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(1\)	\(3\)	\(\frac{ 1}{ 2}\)
\(0\)	\(2\)	\(2\)	\(4\)	\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-72\)	\(64\)	\(16\)	\(8\)

5

New Number: 4.69 | AESZ: 350 | Superseeker: 49 173876/9 | Hash: e6de16eb3758d2ed5687f4b2a2abf36b

Degree: 4

$\theta^4-x\left(24+184\theta+545\theta^2+722\theta^3+289\theta^4\right)+2^{3} 3 x^{2}\left(214\theta^4+2734\theta^3+4861\theta^2+2640\theta+468\right)+2^{6} 3^{2} x^{3}\left(1391\theta^4+5184\theta^3+4252\theta^2+1296\theta+126\right)+2^{10} 3^{6} x^{4}\left((2\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 24, 1944, 232800, 34133400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 49, 136, 173876/9, 781152, 57087750, ... ; Common denominator:...

Discriminant

$(256z-1)(81z-1)(1+24z)^2$

Local exponents

$-\frac{ 1}{ 24}$ $0$ $\frac{ 1}{ 256}$ $\frac{ 1}{ 81}$ $\infty$
$0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $1$ $\frac{ 1}{ 2}$
$3$ $0$ $1$ $1$ $\frac{ 1}{ 2}$
$4$ $0$ $2$ $2$ $\frac{ 1}{ 2}$

\(-\frac{ 1}{ 24}\)	\(0\)	\(\frac{ 1}{ 256}\)	\(\frac{ 1}{ 81}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(0\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)
\(3\)	\(0\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)
\(4\)	\(0\)	\(2\)	\(2\)	\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ 351/4.70

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-64\)	\(60\)	\(18\)	\(8\)

6

New Number: 5.11 | AESZ: 71 | Superseeker: 112 378800 | Hash: cf4de65b0566a4f6294132c167d227eb

Degree: 5

$\theta^4+2^{4} x\left(39\theta^4-42\theta^3-29\theta^2-8\theta-1\right)+2^{11} x^{2}\theta(37\theta^3-137\theta^2-10\theta-1)-2^{16} x^{3}\left(181\theta^4+456\theta^3+353\theta^2+132\theta+19\right)-2^{23} 5 x^{4}\left(36\theta^4+60\theta^3+36\theta^2+6\theta-1\right)+2^{30} 5^{2} x^{5}\left((\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 16, 656, 40192, 3006736, ...
--> OEIS
Normalized instanton numbers (n₀=1): 112, -4570, 378800, -40565898, 5098744272, ... ; Common denominator:...

Discriminant

$(16z-1)(128z-1)(128z+1)(1+320z)^2$

Local exponents

$-\frac{ 1}{ 128}$ $-\frac{ 1}{ 320}$ $0$ $\frac{ 1}{ 128}$ $\frac{ 1}{ 16}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $1$
$1$ $1$ $0$ $1$ $1$ $1$
$1$ $3$ $0$ $1$ $1$ $1$
$2$ $4$ $0$ $2$ $2$ $1$

\(-\frac{ 1}{ 128}\)	\(-\frac{ 1}{ 320}\)	\(0\)	\(\frac{ 1}{ 128}\)	\(\frac{ 1}{ 16}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)
\(1\)	\(3\)	\(0\)	\(1\)	\(1\)	\(1\)
\(2\)	\(4\)	\(0\)	\(2\)	\(2\)	\(1\)

Note:

This is operator "5.11" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(304\)	\(32\)	\(32\)	\(8\)

7

New Number: 5.30 | AESZ: 209 | Superseeker: 478/17 285760/17 | Hash: a03a0a18a8b2a4926d11e4e42b958f98

Degree: 5

$17^{2} \theta^4-2 17 x\left(1902\theta^4+3708\theta^3+2789\theta^2+935\theta+119\right)+2^{2} x^{2}\left(62408\theta^4+68576\theta^3-10029\theta^2-24106\theta-5661\right)-2^{2} x^{3}\left(66180\theta^4+33048\theta^3+20785\theta^2+17799\theta+4794\right)+2^{7} x^{4}(2\theta+1)(196\theta^3+498\theta^2+487\theta+169)-2^{12} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 14, 978, 103820, 13387570, ...
--> OEIS
Normalized instanton numbers (n₀=1): 478/17, 7784/17, 285760/17, 15280156/17, 1006004774/17, ... ; Common denominator:...

Discriminant

$-(16z^3-32z^2+220z-1)(-17+32z)^2$

Local exponents

$0$ ≈$0.004548$ $\frac{ 17}{ 32}$ ≈$0.997726-3.570079I$ ≈$0.997726+3.570079I$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $1$ $1$ $1$
$0$ $1$ $3$ $1$ $1$ $1$
$0$ $2$ $4$ $2$ $2$ $\frac{ 3}{ 2}$

\(0\)	≈\(0.004548\)	\(\frac{ 17}{ 32}\)	≈\(0.997726-3.570079I\)	≈\(0.997726+3.570079I\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(3\)	\(1\)	\(1\)	\(1\)
\(0\)	\(2\)	\(4\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.30" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-108\)	\(62\)	\(17\)	\(8\)

8

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

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

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

Note:

This is operator "5.39" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-72\)	\(56\)	\(20\)	\(8\)

9

New Number: 5.42 | AESZ: 231 | Superseeker: 460/3 894404/3 | Hash: 6f793238336123adfdcd7ee17d64e5ec

Degree: 5

$3^{2} \theta^4-2^{2} 3 x\left(28\theta^4+1016\theta^3+739\theta^2+231\theta+30\right)-2^{9} x^{2}\left(1168\theta^4-968\theta^3-9518\theta^2-5325\theta-1005\right)+2^{16} x^{3}\left(988\theta^4+8208\theta^3-743\theta^2-4230\theta-1245\right)+2^{24} 5 x^{4}(2\theta+1)^2(9\theta^2-279\theta-277)-2^{33} 5^{2} x^{5}(2\theta+1)^2(2\theta+3)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 40, 3240, 313600, 39327400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 460/3, -16828/3, 894404/3, -42271624/3, 2076730720/3, ... ; Common denominator:...

Discriminant

$-(256z-1)(32768z^2-208z+1)(3+640z)^2$

Local exponents

$-\frac{ 3}{ 640}$ $0$ $\frac{ 13}{ 4096}-\frac{ 7}{ 4096}\sqrt{ 7}I$ $\frac{ 13}{ 4096}+\frac{ 7}{ 4096}\sqrt{ 7}I$ $\frac{ 1}{ 256}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $1$ $1$ $\frac{ 1}{ 2}$
$3$ $0$ $1$ $1$ $1$ $\frac{ 3}{ 2}$
$4$ $0$ $2$ $2$ $2$ $\frac{ 3}{ 2}$

\(-\frac{ 3}{ 640}\)	\(0\)	\(\frac{ 13}{ 4096}-\frac{ 7}{ 4096}\sqrt{ 7}I\)	\(\frac{ 13}{ 4096}+\frac{ 7}{ 4096}\sqrt{ 7}I\)	\(\frac{ 1}{ 256}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)
\(3\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 3}{ 2}\)
\(4\)	\(0\)	\(2\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.42" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(160\)	\(48\)	\(24\)	\(8\)

10

New Number: 5.76 | AESZ: 306 | Superseeker: 73/3 11119 | Hash: d14307aa38b16c728ee31e5936937c44

Degree: 5

$3^{2} \theta^4-3 x\left(592\theta^4+1100\theta^3+829\theta^2+279\theta+36\right)+x^{2}\left(13801\theta^4+6652\theta^3-18041\theta^2-14904\theta-3312\right)-2 x^{3}\theta(8461\theta^3-29160\theta^2-28365\theta-7236)-2^{2} 3 7 x^{4}\left(513\theta^4+864\theta^3+487\theta^2+64\theta-16\right)-2^{3} 3 7^{2} x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 12, 732, 67080, 7456140, ...
--> OEIS
Normalized instanton numbers (n₀=1): 73/3, 2131/6, 11119, 518671, 29749701, ... ; Common denominator:...

Discriminant

$-(z+1)(54z^2+189z-1)(-3+14z)^2$

Local exponents

$-\frac{ 7}{ 4}-\frac{ 11}{ 36}\sqrt{ 33}$ $-1$ $0$ $-\frac{ 7}{ 4}+\frac{ 11}{ 36}\sqrt{ 33}$ $\frac{ 3}{ 14}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 2}{ 3}$
$1$ $1$ $0$ $1$ $1$ $1$
$1$ $1$ $0$ $1$ $3$ $1$
$2$ $2$ $0$ $2$ $4$ $\frac{ 4}{ 3}$

\(-\frac{ 7}{ 4}-\frac{ 11}{ 36}\sqrt{ 33}\)	\(-1\)	\(0\)	\(-\frac{ 7}{ 4}+\frac{ 11}{ 36}\sqrt{ 33}\)	\(\frac{ 3}{ 14}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 2}{ 3}\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)
\(1\)	\(1\)	\(0\)	\(1\)	\(3\)	\(1\)
\(2\)	\(2\)	\(0\)	\(2\)	\(4\)	\(\frac{ 4}{ 3}\)

Note:

This is operator "5.76" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-90\)	\(60\)	\(18\)	\(8\)

11

New Number: 8.18 | AESZ: 197 | Superseeker: 3 1621/13 | Hash: 4cc8bdba73e5fa6cb4089fa5296429de

Degree: 8

$13^{2} \theta^4-13^{2} x\left(41\theta^4+82\theta^3+67\theta^2+26\theta+4\right)-2^{3} 13 x^{2}\left(471\theta^4+1788\theta^3+2555\theta^2+1534\theta+338\right)+2^{6} 13 x^{3}\left(251\theta^4+1014\theta^3+1798\theta^2+1413\theta+405\right)+2^{9} x^{4}\left(749\theta^4+436\theta^3-4908\theta^2-6266\theta-2145\right)-2^{12} x^{5}\left(379\theta^4+1270\theta^3+967\theta^2-42\theta-178\right)-2^{15} x^{6}\left(9\theta^4-156\theta^3-273\theta^2-156\theta-28\right)+2^{18} x^{7}\left(13\theta^4+26\theta^3+20\theta^2+7\theta+1\right)-2^{21} x^{8}\left((\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 4, 68, 1552, 43156, ...
--> OEIS
Normalized instanton numbers (n₀=1): 3, 226/13, 1621/13, 20666/13, 289056/13, ... ; Common denominator:...

Discriminant

$-(z-1)(8z+1)(64z^2-48z+1)(-13+64z^2)^2$

Local exponents

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

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

Note:

The operator has a second MUM-point at infinity, corresponding to operator 8.19.

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-88\)	\(-8\)	\(52\)	\(8\)

12

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

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

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

Note:

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

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-172\)	\(-8\)	\(52\)	\(8\)

13

New Number: 1.3 | AESZ: 3 | Superseeker: 32 26016 | Hash: e7a9c334fb603aceccc0517dab63e7d4

Degree: 1

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 16, 1296, 160000, 24010000, ...
--> OEIS
Normalized instanton numbers (n₀=1): 32, 608, 26016, 1606496, 122373984, ... ; Common denominator:...

Discriminant

$1-256z$

Local exponents

$0$ $\frac{ 1}{ 256}$ $\infty$
$0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $\frac{ 1}{ 2}$
$0$ $1$ $\frac{ 1}{ 2}$
$0$ $2$ $\frac{ 1}{ 2}$

\(0\)	\(\frac{ 1}{ 256}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(\frac{ 1}{ 2}\)
\(0\)	\(2\)	\(\frac{ 1}{ 2}\)

Note:

A-incarnation: X(2,2,2,2) in P^7.

\(4.+3.256527087I\)	\(-1-224\lambda\)	\(\frac{ 3}{ 4}+168\lambda\)	\(.44582463e-1-112\lambda\)
\(9\)	\(-2\)	\(\frac{ 9}{ 4}\)	\(-\frac{ 3}{ 4}-168\lambda\)
\(12\)	\(-4\)	\(4\)	\(-1-224\lambda\)
\(36\)	\(-12\)	\(9\)	\(-2.-3.256527087I\)

\(4.+2.209786237I\)	\(-1.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-1.104893119I\)	\(1+152\lambda\)	\(-.171535199-114\lambda\)
\(8\)	\(-3\)	\(\frac{ 8}{ 3}\)	\(-1-152\lambda\)
\(12\)	\(-6\)	\(5\)	\(-1.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-1.104893119I\)
\(24\)	\(-12\)	\(8\)	\(-2.-2.209786237I\)

\(\frac{ 11}{ 2}+600\lambda\)	\(-\frac{ 9}{ 4}-300\lambda\)	\(\frac{ 21}{ 20}+140\lambda\)	\(-.196596398-90\lambda\)
\(14\)	\(-6\)	\(\frac{ 49}{ 15}\)	\(-\frac{ 21}{ 20}-140\lambda\)
\(30\)	\(-15\)	\(8\)	\(-\frac{ 9}{ 4}-300\lambda\)
\(60\)	\(-30\)	\(14\)	\(-\frac{ 7}{ 2}-600\lambda\)

\(1+224\lambda\)	\(0\)	\(56\lambda\)	\(.98194154e-1\)
\(3\)	\(1\)	\(\frac{ 3}{ 4}\)	\(-56\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(12\)	\(0\)	\(3\)	\(1-224\lambda\)

\(-224\lambda\)	\(5\)	\(1\)	\(1\)
\(-3\)	\(-6\)	\(-1\)	\(0\)
\(0\)	\(12\)	\(0\)	\(0\)
\(-12\)	\(0\)	\(0\)	\(0\)

\(1.+1.104893119I\)	\(0\)	\(57\lambda\)	\(\frac{ 276}{ 2713}\)
\(3\)	\(1\)	\(\frac{ 3}{ 4}\)	\(-57\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(12\)	\(0\)	\(3\)	\(1.-1.104893119I\)

\(-\frac{ 1104893119}{ 1000000000}I\)	\(5\)	\(1\)	\(1\)
\(-3\)	\(-6\)	\(-1\)	\(0\)
\(0\)	\(12\)	\(0\)	\(0\)
\(-12\)	\(0\)	\(0\)	\(0\)

\(1+150\lambda\)	\(0\)	\(\frac{ 55}{ 2}\lambda\)	\(.35225900e-1\)
\(\frac{ 11}{ 4}\)	\(1\)	\(\frac{ 121}{ 240}\)	\(-\frac{ 55}{ 2}\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(15\)	\(0\)	\(\frac{ 11}{ 4}\)	\(1-150\lambda\)

\(-150\lambda\)	\(\frac{ 21}{ 4}\)	\(1\)	\(1\)
\(-\frac{ 11}{ 4}\)	\(-\frac{ 15}{ 2}\)	\(-1\)	\(0\)
\(0\)	\(15\)	\(0\)	\(0\)
\(-15\)	\(0\)	\(0\)	\(0\)

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:

Explicit solution

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)

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: