Calabi-Yau differential operator database v.3.0

1

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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2

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 $B\ast g$.

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

3

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 ...

4

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 ...

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

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

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

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

Calabi-Yau differential operator database v.3

Summary

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:

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

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

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

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