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 $C\ast c$

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

2

New Number: 2.22 | AESZ: 135 | Superseeker: 36 -206716/3 | Hash: 85e55291bd94bb32087b43f104c60645

Degree: 2

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 36, 3780, 388080, 8108100, ...
--> OEIS
Normalized instanton numbers (n₀=1): 36, -477, -206716/3, -4431924, -27005472, ... ; Common denominator:...

Discriminant

$1-576z+110592z^2$

Local exponents

$0$ $\frac{ 1}{ 384}-\frac{ 1}{ 1152}\sqrt{ 3}I$ $\frac{ 1}{ 384}+\frac{ 1}{ 1152}\sqrt{ 3}I$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$0$ $1$ $1$ $\frac{ 3}{ 4}$
$0$ $1$ $1$ $\frac{ 5}{ 4}$
$0$ $2$ $2$ $\frac{ 7}{ 4}$

\(0\)	\(\frac{ 1}{ 384}-\frac{ 1}{ 1152}\sqrt{ 3}I\)	\(\frac{ 1}{ 384}+\frac{ 1}{ 1152}\sqrt{ 3}I\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 3}{ 4}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 5}{ 4}\)
\(0\)	\(2\)	\(2\)	\(\frac{ 7}{ 4}\)

Integral instantons: Hadamard, product, $C, \ast, f$.,...
Coefficients of the Yukawa coupling: 1, 36, -3780, -1860408, -283646916, -3375683964, 8182006866936, 1873126855818072,...
Coefficients of the q-coordinate : 0, 1, -156, 22446, -2570800, 297228021, -32847734088, 3343576302482,...

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

No topological data

Monodromy (with respect to Frobenius basis)

$1$	$-1$	$\frac{ 1}{ 2}$	$-\frac{ 1}{ 6}$
$0$	$1$	$-1$	$\frac{ 1}{ 2}$
$0$	$0$	$1$	$-1$
$0$	$0$	$0$	$1$

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$\frac{ 5}{ 24}+Itan(\frac{ 801}{ 812})$	$-\frac{ 19}{ 144}+52\lambda$	$-\frac{ 323}{ 1728}+\frac{ 221}{ 3}\lambda$	$.92182440e-1+\frac{ 247}{ 9}\lambda$
$\frac{ 17}{ 4}+\frac{ 9}{ 1000000000}I$	$\frac{ 41}{ 24}-\frac{ 3}{ 1000000000}I$	$\frac{ 289}{ 288}-\frac{ 1}{ 250000000}I$	$\frac{ 323}{ 1728}-\frac{ 221}{ 3}\lambda$
$-3-\frac{ 3}{ 500000000}I$	$-\frac{ 1}{ 2}+\frac{ 1}{ 500000000}I$	$\frac{ 7}{ 24}+\frac{ 3}{ 1000000000}I$	$-\frac{ 19}{ 144}+52\lambda$
$18.000000018+.41e-7I$	$3.000000039-.12000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7I$	$\frac{ 17}{ 4}-\frac{ 9}{ 500000000}I$	$\frac{ 43}{ 24}-Itan(\frac{ 801}{ 812})$

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$\frac{ 43}{ 24}+Itan(\frac{ 801}{ 812})$	$-\frac{ 19}{ 144}-52\lambda$	$\frac{ 323}{ 1728}+\frac{ 221}{ 3}\lambda$	$.92182440e-1-\frac{ 247}{ 9}\lambda$
$\frac{ 17}{ 4}$	$\frac{ 7}{ 24}$	$\frac{ 289}{ 288}$	$-\frac{ 323}{ 1728}-\frac{ 221}{ 3}\lambda$
$3$	$-\frac{ 1}{ 2}$	$\frac{ 41}{ 24}$	$-\frac{ 19}{ 144}-52\lambda$
$18$	$-3$	$\frac{ 17}{ 4}$	$\frac{ 5}{ 24}-Itan(\frac{ 801}{ 812})$

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Basis of the Doran-Morgan lattice

$\frac{ 19}{ 24}-\frac{ 1162393719353719131361189363784404603456366390101814206736549803033200099854000208071729302850101578}{ 768799759549186043811713254203741173211443985818991590275710787225120378790852066470688698366857287}I$	$\frac{ 8750000003}{ 1000000000}+\frac{ 113}{ 6000000000}I$	$\frac{ 378000000701999998397}{ 324000000648000002005}+\frac{ 1707000001584}{ 324000000648000002005}I$	$1$
$-\frac{ 17}{ 4}-\frac{ 9}{ 1000000000}I$	$-\frac{ 12000000009}{ 1000000000}-\frac{ 53}{ 2000000000}I$	$-\frac{ 324000000647999998643}{ 324000000648000002005}-\frac{ 1476000001476}{ 324000000648000002005}I$	$0$
$3+\frac{ 3}{ 500000000}I$	$\frac{ 9000000009}{ 500000000}+\frac{ 41}{ 1000000000}I$	$0$	$0$
$-\frac{ 9000000009}{ 500000000}-\frac{ 41}{ 1000000000}I$	$0$	$0$	$0$

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3

New Number: 2.25 | AESZ: 138 | Superseeker: 27 2618 | Hash: c524254b716132352b27914640b03c8b

Degree: 2

$\theta^4-3 x(3\theta+1)(3\theta+2)(17\theta^2+17\theta+6)+2^{3} 3^{4} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 36, 3780, 524160, 82952100, ...
--> OEIS
Normalized instanton numbers (n₀=1): 27, 189/4, 2618, 43713, 2319057, ... ; Common denominator:...

Discriminant

$(243z-1)(216z-1)$

Local exponents

$0$ $\frac{ 1}{ 243}$ $\frac{ 1}{ 216}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 3}$
$0$ $1$ $1$ $\frac{ 2}{ 3}$
$0$ $1$ $1$ $\frac{ 4}{ 3}$
$0$ $2$ $2$ $\frac{ 5}{ 3}$

\(0\)	\(\frac{ 1}{ 243}\)	\(\frac{ 1}{ 216}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 3}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 2}{ 3}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 4}{ 3}\)
\(0\)	\(2\)	\(2\)	\(\frac{ 5}{ 3}\)

Note:

Hadamard product $B\ast g$.

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-156\)	\(108\)	\(36\)	\(15\)

4

New Number: 2.7 | AESZ: 51 | Superseeker: 92 585396 | Hash: e09b9b149b6845daa8d5ef03df33f22d

Degree: 2

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 36, 7980, 2716560, 1127025900, ...
--> OEIS
Normalized instanton numbers (n₀=1): 92, 5052, 585396, 99982012, 21054159152, ... ; Common denominator:...

Discriminant

$1-704z-4096z^2$

Local exponents

$-\frac{ 11}{ 128}-\frac{ 5}{ 128}\sqrt{ 5}$ $0$ $-\frac{ 11}{ 128}+\frac{ 5}{ 128}\sqrt{ 5}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$1$ $0$ $1$ $\frac{ 3}{ 4}$
$1$ $0$ $1$ $\frac{ 5}{ 4}$
$2$ $0$ $2$ $\frac{ 7}{ 4}$

\(-\frac{ 11}{ 128}-\frac{ 5}{ 128}\sqrt{ 5}\)	\(0\)	\(-\frac{ 11}{ 128}+\frac{ 5}{ 128}\sqrt{ 5}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 3}{ 4}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 5}{ 4}\)
\(2\)	\(0\)	\(2\)	\(\frac{ 7}{ 4}\)

Note:

Hadamard product C*b
Related to 8.139
A-Incarnation: double cover of $B_5$.

A:Incarnation: double cover of B

Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 92, 40508, 15805784, 6398889276, 2631769894092, 1095690103233560, 460102352983654760,...
Coefficients of the q-coordinate : 0, 1, -180, 9766, -918864, -84667391, -28201300344, -8416763367758,...

	Gopakumar-Vafa invariants
g=0	920, 50520, 5853960, 999820120, 210541591520, 50726392934600, 13414062769202760, 3797984131204286040,...
g=1	0, 3, -1840, 340009, 1947267584, 1647668876313, 1015529214081408, 546679951529049217,...
g=2	,...

Explicit solution

$A_{n}=\dbinom{2n}{n}\dbinom{4n}{2n}\sum_{k=0}^{n}\dbinom{n}{k}^2\dbinom{n+k}{n}$

Maple LaTex

Characteristic classes:

$C_3$	$C_2 H$	$H^3$	$ \vert H \vert$
$-200$	$64$	$10$	$7$

Monodromy (with respect to Frobenius basis)

$5.6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667+3.876817960I$	$-2.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-1.938408980I$	$\frac{ 133}{ 90}+\frac{ 760}{ 3}\lambda$	$-.168701507-.904590857I$
$\frac{ 38}{ 3}$	$-\frac{ 16}{ 3}$	$\frac{ 361}{ 90}$	$-\frac{ 133}{ 90}-\frac{ 760}{ 3}\lambda$
$20$	$-10$	$\frac{ 22}{ 3}$	$-2.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-1.938408980I$
$40$	$-20$	$\frac{ 38}{ 3}$	$-3.6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667-3.876817960I$

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$1$	$-1$	$\frac{ 1}{ 2}$	$-\frac{ 1}{ 6}$
$0$	$1$	$-1$	$\frac{ 1}{ 2}$
$0$	$0$	$1$	$-1$
$0$	$0$	$0$	$1$

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$1.+.969204490I$	$0$	$\frac{ 160}{ 3}\lambda$	$.93935734e-1$
$\frac{ 8}{ 3}$	$1$	$\frac{ 32}{ 45}$	$-\frac{ 160}{ 3}\lambda$
$0$	$0$	$1$	$0$
$10$	$0$	$\frac{ 8}{ 3}$	$1.-.969204490I$

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Basis of the Doran-Morgan lattice

$-\frac{ 96920449}{ 100000000}I$	$\frac{ 13}{ 3}$	$1$	$1$
$-\frac{ 8}{ 3}$	$-5$	$-1$	$0$
$0$	$10$	$0$	$0$
$-10$	$0$	$0$	$0$

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5

New Number: 5.130 | AESZ: | Superseeker: 108 122756 | Hash: 829aca3d7a00547e299bf794c8643162

Degree: 5

$\theta^4-2^{2} 3 x\left(12\theta^4+96\theta^3+71\theta^2+23\theta+3\right)-2^{4} 3^{3} x^{2}\left(160\theta^4+64\theta^3-544\theta^2-340\theta-65\right)+2^{8} 3^{5} x^{3}\left(32\theta^4+576\theta^3+588\theta^2+240\theta+35\right)+2^{12} 3^{7} x^{4}(28\theta^2+52\theta+31)(2\theta+1)^2+2^{16} 3^{9} x^{5}(2\theta+1)^2(2\theta+3)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 36, 3780, 558000, 98828100, ...
--> OEIS
Normalized instanton numbers (n₀=1): 108, -1782, 122756, -5930658, 607239072, ... ; Common denominator:...

Discriminant

$(144z-1)(6912z^2+288z-1)(1+144z)^2$

Local exponents

$-\frac{ 1}{ 48}-\frac{ 1}{ 72}\sqrt{ 3}$ $-\frac{ 1}{ 144}$ $0$ $-\frac{ 1}{ 48}+\frac{ 1}{ 72}\sqrt{ 3}$ $\frac{ 1}{ 144}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $0$ $1$ $1$ $\frac{ 1}{ 2}$
$1$ $3$ $0$ $1$ $1$ $\frac{ 3}{ 2}$
$2$ $4$ $0$ $2$ $2$ $\frac{ 3}{ 2}$

\(-\frac{ 1}{ 48}-\frac{ 1}{ 72}\sqrt{ 3}\)	\(-\frac{ 1}{ 144}\)	\(0\)	\(-\frac{ 1}{ 48}+\frac{ 1}{ 72}\sqrt{ 3}\)	\(\frac{ 1}{ 144}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)
\(1\)	\(3\)	\(0\)	\(1\)	\(1\)	\(\frac{ 3}{ 2}\)
\(2\)	\(4\)	\(0\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.130" from ...

6

New Number: 5.134 | AESZ: | Superseeker: 176 1215248/3 | Hash: 5bd656df18dc5d02b2f2a068ba88ab74

Degree: 5

$\theta^4+2^{2} x\left(4\theta^4-352\theta^3-250\theta^2-74\theta-9\right)-2^{4} 3 x^{2}\left(3168\theta^4+5952\theta^3-3712\theta^2-2648\theta-519\right)-2^{8} 3^{3} x^{3}\left(2912\theta^4-3008\theta^3-3152\theta^2-1160\theta-145\right)+2^{12} 3^{3} 5 x^{4}(2\theta+1)(824\theta^3+1668\theta^2+1342\theta+405)+2^{16} 3^{4} 5^{2} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 36, 4572, 918000, 228519900, ...
--> OEIS
Normalized instanton numbers (n₀=1): 176, -3238, 1215248/3, -18807038, 3651829680, ... ; Common denominator:...

Discriminant

$(48z-1)(432z-1)(16z+1)(1+240z)^2$

Local exponents

$-\frac{ 1}{ 16}$ $-\frac{ 1}{ 240}$ $0$ $\frac{ 1}{ 432}$ $\frac{ 1}{ 48}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $0$ $1$ $1$ $\frac{ 5}{ 6}$
$1$ $3$ $0$ $1$ $1$ $\frac{ 7}{ 6}$
$2$ $4$ $0$ $2$ $2$ $\frac{ 3}{ 2}$

\(-\frac{ 1}{ 16}\)	\(-\frac{ 1}{ 240}\)	\(0\)	\(\frac{ 1}{ 432}\)	\(\frac{ 1}{ 48}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(\frac{ 5}{ 6}\)
\(1\)	\(3\)	\(0\)	\(1\)	\(1\)	\(\frac{ 7}{ 6}\)
\(2\)	\(4\)	\(0\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

B-incarnation as fibre product 61131- x 182--1

7

New Number: 5.65 | AESZ: 273 | Superseeker: 63/5 14016/5 | Hash: cf49bc645cb0404ce7bc9ca1d41d3152

Degree: 5

$5^{2} \theta^4-3 5 x\left(333\theta^4+882\theta^3+781\theta^2+340\theta+60\right)+2^{2} 3^{2} x^{2}\left(5184\theta^4+40662\theta^3+71829\theta^2+47700\theta+11540\right)+2^{2} 3^{5} x^{3}\left(8424\theta^4+9720\theta^3-46899\theta^2-63045\theta-21260\right)-2^{4} 3^{8} x^{4}\left(1296\theta^4+12312\theta^3+23094\theta^2+16263\theta+3956\right)-2^{6} 3^{11} x^{5}(3\theta+2)(3\theta+4)(6\theta+5)(6\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 36, 2196, 161280, 13032900, ...
--> OEIS
Normalized instanton numbers (n₀=1): 63/5, -747/4, 14016/5, -55584, 6071598/5, ... ; Common denominator:...

Discriminant

$-(-1+27z)(108z+5)^2(108z-1)^2$

Local exponents

$-\frac{ 5}{ 108}$ $0$ $\frac{ 1}{ 108}$ $\frac{ 1}{ 27}$ $\infty$
$0$ $0$ $0$ $0$ $\frac{ 2}{ 3}$
$1$ $0$ $\frac{ 1}{ 6}$ $1$ $\frac{ 5}{ 6}$
$3$ $0$ $\frac{ 5}{ 6}$ $1$ $\frac{ 7}{ 6}$
$4$ $0$ $1$ $2$ $\frac{ 4}{ 3}$

\(-\frac{ 5}{ 108}\)	\(0\)	\(\frac{ 1}{ 108}\)	\(\frac{ 1}{ 27}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 2}{ 3}\)
\(1\)	\(0\)	\(\frac{ 1}{ 6}\)	\(1\)	\(\frac{ 5}{ 6}\)
\(3\)	\(0\)	\(\frac{ 5}{ 6}\)	\(1\)	\(\frac{ 7}{ 6}\)
\(4\)	\(0\)	\(1\)	\(2\)	\(\frac{ 4}{ 3}\)

Note:

This is operator "5.65" from ...

8

New Number: 13.9 | AESZ: | Superseeker: 8 2200/9 | Hash: 31ff3b7bd4c8fed070ee43b6903d3752

Degree: 13

$\theta^4+2^{3} x\theta(4\theta^3-8\theta^2-5\theta-1)-2^{4} x^{2}\left(48\theta^4+120\theta^3+45\theta^2+74\theta+36\right)-2^{7} x^{3}\left(101\theta^4-342\theta^3-387\theta^2-410\theta-171\right)+2^{8} x^{4}\left(3121\theta^4+14104\theta^3+30889\theta^2+27720\theta+9351\right)+2^{11} 3^{2} x^{5}\left(655\theta^4+4062\theta^3+10081\theta^2+10272\theta+3856\right)-2^{12} 3^{2} x^{6}\left(2272\theta^4+2816\theta^3-9950\theta^2-18768\theta-8813\right)-2^{15} 3^{3} x^{7}\left(1546\theta^4+12172\theta^3+30708\theta^2+33880\theta+13843\right)+2^{16} 3^{4} x^{8}\left(1099\theta^4+1344\theta^3-11134\theta^2-23964\theta-13063\right)+2^{19} 3^{5} x^{9}\left(458\theta^4+4828\theta^3+15325\theta^2+19721\theta+8830\right)-2^{20} 3^{6} x^{10}(\theta+1)(368\theta^3+1752\theta^2+1297\theta-1035)-2^{23} 3^{7} x^{11}(\theta+1)(\theta+2)(39\theta^2+513\theta+1172)+2^{24} 3^{9} x^{12}(\theta+3)(\theta+2)(\theta+1)(17\theta+82)-2^{27} 3^{10} x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 0, 36, -192, -4284, ...
--> OEIS
Normalized instanton numbers (n₀=1): 8, -75/2, 2200/9, -8117/2, 47936, ... ; Common denominator:...

Discriminant

$-(8z+1)(5184z^3+432z^2-36z+1)(12z+1)^2(144z^2-24z-1)^2(4z-1)^3$

Local exponents

≈$-0.141868$ $-\frac{ 1}{ 8}$ $-\frac{ 1}{ 12}$ $\frac{ 1}{ 12}-\frac{ 1}{ 12}\sqrt{ 2}$ $0$ ≈$0.029267-0.022431I$ ≈$0.029267+0.022431I$ $\frac{ 1}{ 12}+\frac{ 1}{ 12}\sqrt{ 2}$ $\frac{ 1}{ 4}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $1$
$1$ $1$ $\frac{ 1}{ 2}$ $1$ $0$ $1$ $1$ $1$ $\frac{ 1}{ 2}$ $2$
$1$ $1$ $\frac{ 1}{ 2}$ $3$ $0$ $1$ $1$ $3$ $\frac{ 3}{ 2}$ $3$
$2$ $2$ $1$ $4$ $0$ $2$ $2$ $4$ $2$ $4$

≈\(-0.141868\)	\(-\frac{ 1}{ 8}\)	\(-\frac{ 1}{ 12}\)	\(\frac{ 1}{ 12}-\frac{ 1}{ 12}\sqrt{ 2}\)	\(0\)	≈\(0.029267-0.022431I\)	≈\(0.029267+0.022431I\)	\(\frac{ 1}{ 12}+\frac{ 1}{ 12}\sqrt{ 2}\)	\(\frac{ 1}{ 4}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(1\)	\(\frac{ 1}{ 2}\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)	\(2\)
\(1\)	\(1\)	\(\frac{ 1}{ 2}\)	\(3\)	\(0\)	\(1\)	\(1\)	\(3\)	\(\frac{ 3}{ 2}\)	\(3\)
\(2\)	\(2\)	\(1\)	\(4\)	\(0\)	\(2\)	\(2\)	\(4\)	\(2\)	\(4\)

Note:

This is operator "13.9" from ...

9

New Number: 14.8 | AESZ: | Superseeker: 92/5 -76/5 | Hash: a787adbb87527c14af9a5f2508991317

Degree: 14

\(5^{2} \theta^4-2^{2} 5 x\left(244\theta^4+496\theta^3+473\theta^2+225\theta+45\right)+2^{4} x^{2}\left(24144\theta^4+95872\theta^3+155244\theta^2+117660\theta+36835\right)-2^{9} x^{3}\left(33248\theta^4+180880\theta^3+407234\theta^2+416430\theta+168275\right)+2^{14} x^{4}\left(32428\theta^4+181000\theta^3+474021\theta^2+605903\theta+294817\right)-2^{19} x^{5}\left(29162\theta^4+130236\theta^3+270865\theta^2+378135\theta+208235\right)+2^{24} x^{6}\left(25019\theta^4+101558\theta^3+110864\theta^2+69739\theta+20552\right)-2^{29} x^{7}\left(17583\theta^4+76998\theta^3+91248\theta^2+4717\theta-39868\right)+2^{34} x^{8}\left(10081\theta^4+40990\theta^3+72600\theta^2+35261\theta-9816\right)-2^{39} x^{9}\left(5407\theta^4+16538\theta^3+33406\theta^2+27573\theta+6100\right)+2^{44} x^{10}\left(2699\theta^4+7862\theta^3+13380\theta^2+11845\theta+4325\right)-2^{49} x^{11}\left(1033\theta^4+3966\theta^3+6998\theta^2+6213\theta+2329\right)+2^{54} x^{12}\left(255\theta^4+1318\theta^3+2815\theta^2+2864\theta+1159\right)-2^{59} x^{13}\left(35\theta^4+230\theta^3+589\theta^2+692\theta+313\right)+2^{65} x^{14}\left((\theta+2)^4\right)\)

Maple LaTex

Coefficients of the holomorphic solution: 1, 36, 1196, 41488, 1543916, ...
--> OEIS
Normalized instanton numbers (n₀=1): 92/5, -342/5, -76/5, 75394/5, -2156752/5, ... ; Common denominator:...

Discriminant

$(64z-1)(32z-1)(256z^2-48z+1)(32768z^3-1024z^2-5-32z)^2(16z-1)^4$

Local exponents

≈$-0.020941-0.040594I$ ≈$-0.020941+0.040594I$ $0$ $\frac{ 1}{ 64}$ $\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}$ $\frac{ 1}{ 32}$ $\frac{ 1}{ 16}$ ≈$0.073133$ $\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $-\frac{ 1}{ 2}$ $0$ $0$ $2$
$1$ $1$ $0$ $1$ $1$ $1$ $-\frac{ 1}{ 2}$ $1$ $1$ $2$
$3$ $3$ $0$ $1$ $1$ $1$ $\frac{ 1}{ 2}$ $3$ $1$ $2$
$4$ $4$ $0$ $2$ $2$ $2$ $\frac{ 1}{ 2}$ $4$ $2$ $2$

≈\(-0.020941-0.040594I\)	≈\(-0.020941+0.040594I\)	\(0\)	\(\frac{ 1}{ 64}\)	\(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\)	\(\frac{ 1}{ 32}\)	\(\frac{ 1}{ 16}\)	≈\(0.073133\)	\(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(-\frac{ 1}{ 2}\)	\(0\)	\(0\)	\(2\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(-\frac{ 1}{ 2}\)	\(1\)	\(1\)	\(2\)
\(3\)	\(3\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)	\(3\)	\(1\)	\(2\)
\(4\)	\(4\)	\(0\)	\(2\)	\(2\)	\(2\)	\(\frac{ 1}{ 2}\)	\(4\)	\(2\)	\(2\)

Note:

This is operator "14.8" from ...

10

New Number: 8.25 | AESZ: 299 | Superseeker: -54 -197216/3 | Hash: c9e3907e21d64cf5564bf2d00992459e

Degree: 8

$\theta^4-2 3 x\left(144\theta^4+36\theta^3+47\theta^2+29\theta+6\right)+2^{2} 3^{2} x^{2}\left(8376\theta^4+6648\theta^3+8157\theta^2+3900\theta+724\right)-2^{4} 3^{4} x^{3}\left(42672\theta^4+68616\theta^3+81056\theta^2+44841\theta+9964\right)+2^{6} 3^{5} x^{4}\left(374028\theta^4+962040\theta^3+1262091\theta^2+794463\theta+195335\right)-2^{8} 3^{7} x^{5}\left(633840\theta^4+2243328\theta^3+3405968\theta^2+2385208\theta+629129\right)+2^{12} 3^{8} x^{6}\left(438960\theta^4+1884384\theta^3+3176664\theta^2+2380392\theta+652943\right)-2^{19} 3^{10} x^{7}\left(5760\theta^4+25128\theta^3+39548\theta^2+26606\theta+6517\right)+2^{22} 3^{11} x^{8}(6\theta+5)^2(6\theta+7)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 36, 1908, 116496, 7816500, ...
--> OEIS
Normalized instanton numbers (n₀=1): -54, -1530, -197216/3, -3553920, -222887448, ... ; Common denominator:...

Discriminant

$(1-144z+6912z^2)(108z-1)^2(3456z^2-252z+1)^2$

Local exponents

$0$ $\frac{ 7}{ 192}-\frac{ 1}{ 576}\sqrt{ 345}$ $\frac{ 1}{ 108}$ $\frac{ 1}{ 96}-\frac{ 1}{ 288}\sqrt{ 3}I$ $\frac{ 1}{ 96}+\frac{ 1}{ 288}\sqrt{ 3}I$ $\frac{ 7}{ 192}+\frac{ 1}{ 576}\sqrt{ 345}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $\frac{ 5}{ 6}$
$0$ $1$ $\frac{ 1}{ 2}$ $1$ $1$ $1$ $\frac{ 5}{ 6}$
$0$ $3$ $\frac{ 1}{ 2}$ $1$ $1$ $3$ $\frac{ 7}{ 6}$
$0$ $4$ $1$ $2$ $2$ $4$ $\frac{ 7}{ 6}$

\(0\)	\(\frac{ 7}{ 192}-\frac{ 1}{ 576}\sqrt{ 345}\)	\(\frac{ 1}{ 108}\)	\(\frac{ 1}{ 96}-\frac{ 1}{ 288}\sqrt{ 3}I\)	\(\frac{ 1}{ 96}+\frac{ 1}{ 288}\sqrt{ 3}I\)	\(\frac{ 7}{ 192}+\frac{ 1}{ 576}\sqrt{ 345}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 5}{ 6}\)
\(0\)	\(1\)	\(\frac{ 1}{ 2}\)	\(1\)	\(1\)	\(1\)	\(\frac{ 5}{ 6}\)
\(0\)	\(3\)	\(\frac{ 1}{ 2}\)	\(1\)	\(1\)	\(3\)	\(\frac{ 7}{ 6}\)
\(0\)	\(4\)	\(1\)	\(2\)	\(2\)	\(4\)	\(\frac{ 7}{ 6}\)

Note:

This is operator "8.25" from ...

11

New Number: 8.78 | AESZ: | Superseeker: 52 48732 | Hash: 2fb524ad6efb19e0117ae7acbd9f67b9

Degree: 8

$\theta^4-2^{2} x\left(184\theta^4+224\theta^3+175\theta^2+63\theta+9\right)+2^{4} 3 x^{2}\left(3472\theta^4+9664\theta^3+9864\theta^2+4264\theta+705\right)-2^{8} 3^{2} x^{3}\left(1936\theta^4+27936\theta^3+43336\theta^2+21528\theta+3933\right)-2^{16} 3^{3} x^{4}\left(1384\theta^4+524\theta^3-4555\theta^2-3404\theta-753\right)+2^{19} 3^{4} x^{5}\left(3440\theta^4+13712\theta^3-58\theta^2-3774\theta-1161\right)+2^{22} 3^{5} x^{6}\left(11312\theta^4-9888\theta^3-10808\theta^2-1608\theta+459\right)-2^{26} 3^{7} x^{7}(2\theta+1)(1336\theta^3+2772\theta^2+2234\theta+663)-2^{32} 3^{9} x^{8}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 36, 3780, 555120, 95199300, ...
--> OEIS
Normalized instanton numbers (n₀=1): 52, -399, 48732, -992750, 98106208, ... ; Common denominator:...

Discriminant

$-(256z-1)(110592z^3+6912z^2-288z+1)(-1+96z+13824z^2)^2$

Local exponents

≈$-0.091906$ $-\frac{ 1}{ 288}-\frac{ 1}{ 288}\sqrt{ 7}$ $0$ ≈$0.00385$ $\frac{ 1}{ 256}$ $-\frac{ 1}{ 288}+\frac{ 1}{ 288}\sqrt{ 7}$ ≈$0.025556$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $0$ $1$ $1$ $1$ $1$ $\frac{ 3}{ 4}$
$1$ $3$ $0$ $1$ $1$ $3$ $1$ $\frac{ 5}{ 4}$
$2$ $4$ $0$ $2$ $2$ $4$ $2$ $\frac{ 3}{ 2}$

≈\(-0.091906\)	\(-\frac{ 1}{ 288}-\frac{ 1}{ 288}\sqrt{ 7}\)	\(0\)	≈\(0.00385\)	\(\frac{ 1}{ 256}\)	\(-\frac{ 1}{ 288}+\frac{ 1}{ 288}\sqrt{ 7}\)	≈\(0.025556\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(\frac{ 3}{ 4}\)
\(1\)	\(3\)	\(0\)	\(1\)	\(1\)	\(3\)	\(1\)	\(\frac{ 5}{ 4}\)
\(2\)	\(4\)	\(0\)	\(2\)	\(2\)	\(4\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "8.78" from ...

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.

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

\(\frac{ 5}{ 24}+Itan(\frac{ 801}{ 812})\)	\(-\frac{ 19}{ 144}+52\lambda\)	\(-\frac{ 323}{ 1728}+\frac{ 221}{ 3}\lambda\)	\(.92182440e-1+\frac{ 247}{ 9}\lambda\)
\(\frac{ 17}{ 4}+\frac{ 9}{ 1000000000}I\)	\(\frac{ 41}{ 24}-\frac{ 3}{ 1000000000}I\)	\(\frac{ 289}{ 288}-\frac{ 1}{ 250000000}I\)	\(\frac{ 323}{ 1728}-\frac{ 221}{ 3}\lambda\)
\(-3-\frac{ 3}{ 500000000}I\)	\(-\frac{ 1}{ 2}+\frac{ 1}{ 500000000}I\)	\(\frac{ 7}{ 24}+\frac{ 3}{ 1000000000}I\)	\(-\frac{ 19}{ 144}+52\lambda\)
\(18.000000018+.41e-7I\)	\(3.000000039-.12000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7I\)	\(\frac{ 17}{ 4}-\frac{ 9}{ 500000000}I\)	\(\frac{ 43}{ 24}-Itan(\frac{ 801}{ 812})\)

\(\frac{ 43}{ 24}+Itan(\frac{ 801}{ 812})\)	\(-\frac{ 19}{ 144}-52\lambda\)	\(\frac{ 323}{ 1728}+\frac{ 221}{ 3}\lambda\)	\(.92182440e-1-\frac{ 247}{ 9}\lambda\)
\(\frac{ 17}{ 4}\)	\(\frac{ 7}{ 24}\)	\(\frac{ 289}{ 288}\)	\(-\frac{ 323}{ 1728}-\frac{ 221}{ 3}\lambda\)
\(3\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 41}{ 24}\)	\(-\frac{ 19}{ 144}-52\lambda\)
\(18\)	\(-3\)	\(\frac{ 17}{ 4}\)	\(\frac{ 5}{ 24}-Itan(\frac{ 801}{ 812})\)

\(\frac{ 19}{ 24}-\frac{ 1162393719353719131361189363784404603456366390101814206736549803033200099854000208071729302850101578}{ 768799759549186043811713254203741173211443985818991590275710787225120378790852066470688698366857287}I\)	\(\frac{ 8750000003}{ 1000000000}+\frac{ 113}{ 6000000000}I\)	\(\frac{ 378000000701999998397}{ 324000000648000002005}+\frac{ 1707000001584}{ 324000000648000002005}I\)	\(1\)
\(-\frac{ 17}{ 4}-\frac{ 9}{ 1000000000}I\)	\(-\frac{ 12000000009}{ 1000000000}-\frac{ 53}{ 2000000000}I\)	\(-\frac{ 324000000647999998643}{ 324000000648000002005}-\frac{ 1476000001476}{ 324000000648000002005}I\)	\(0\)
\(3+\frac{ 3}{ 500000000}I\)	\(\frac{ 9000000009}{ 500000000}+\frac{ 41}{ 1000000000}I\)	\(0\)	\(0\)
\(-\frac{ 9000000009}{ 500000000}-\frac{ 41}{ 1000000000}I\)	\(0\)	\(0\)	\(0\)

\(.84386396e-1+.881341465I\)	\(-.593907697+1.816219110I\)	\(.987405021+.251865740I\)	\(-.18197034e-1-.280246794I\)
\(-.610146073+4.105015738I\)	\(3.086102688+5.881005017I\)	\(\frac{ 1}{ ln}(2)^{ \frac{ 8}{ 3}}ln(3)^{ \frac{ 8}{ 5}}Zeta(5)^8-1.317777791I\)	\(-.605925748-.688412508I\)
\(-1.084750363+4.722447485I\)	\(1.891556916+7.035664131I\)	\(4.676916900-1.255046419I\)	\(-.642466556-.856579334I\)
\(-4.881168587+32.840125900I\)	\(16.688821505+47.048040140I\)	\(24.445126799-10.542222328I\)	\(-3.847405984-5.507300063I\)

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

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

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

\(1.+.755979502I\)	\(0\)	\(\frac{ 39}{ 2}\lambda\)	\(.15875139e-1\)
\(\frac{ 9}{ 2}\)	\(1\)	\(\frac{ 9}{ 16}\)	\(-\frac{ 39}{ 2}\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(36\)	\(0\)	\(\frac{ 9}{ 2}\)	\(1.-.755979502I\)

\(-\frac{ 377989751}{ 500000000}I\)	\(\frac{ 21}{ 2}\)	\(1\)	\(1\)
\(-\frac{ 9}{ 2}\)	\(-18\)	\(-1\)	\(0\)
\(0\)	\(36\)	\(0\)	\(0\)
\(-36\)	\(0\)	\(0\)	\(0\)

\(5.6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667+3.876817960I\)	\(-2.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-1.938408980I\)	\(\frac{ 133}{ 90}+\frac{ 760}{ 3}\lambda\)	\(-.168701507-.904590857I\)
\(\frac{ 38}{ 3}\)	\(-\frac{ 16}{ 3}\)	\(\frac{ 361}{ 90}\)	\(-\frac{ 133}{ 90}-\frac{ 760}{ 3}\lambda\)
\(20\)	\(-10\)	\(\frac{ 22}{ 3}\)	\(-2.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-1.938408980I\)
\(40\)	\(-20\)	\(\frac{ 38}{ 3}\)	\(-3.6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667-3.876817960I\)

\(1.+.969204490I\)	\(0\)	\(\frac{ 160}{ 3}\lambda\)	\(.93935734e-1\)
\(\frac{ 8}{ 3}\)	\(1\)	\(\frac{ 32}{ 45}\)	\(-\frac{ 160}{ 3}\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(10\)	\(0\)	\(\frac{ 8}{ 3}\)	\(1.-.969204490I\)

\(-\frac{ 96920449}{ 100000000}I\)	\(\frac{ 13}{ 3}\)	\(1\)	\(1\)
\(-\frac{ 8}{ 3}\)	\(-5\)	\(-1\)	\(0\)
\(0\)	\(10\)	\(0\)	\(0\)
\(-10\)	\(0\)	\(0\)	\(0\)

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

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:

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:

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:

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:

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