Calabi-Yau differential operator database v.3.0

1

New Number: 1.10 | AESZ: 10 | Superseeker: 928 170869536 | Hash: 51f8135aba94201bd0bbe9b2287a92d5

Degree: 1

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

Coefficients of the holomorphic solution: 1, 144, 176400, 341510400, 811620810000, ...
--> OEIS
Normalized instanton numbers (n₀=1): 928, 245616, 170869536, 174999877936, 221984814405088, ... ; Common denominator:...

Discriminant

No data for singularities

Note:

A-incarnation: X(4,4) in P^5(1,1,1,1,2,2)

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-144\)	\(40\)	\(4\)	\(4\)

2

New Number: 1.11 | AESZ: 11 | Superseeker: 324 10792428 | Hash: 8ac8b98b80383c9f0ea125ccd6e6a55d

Degree: 1

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 72, 37800, 31046400, 31216185000, ...
--> OEIS
Normalized instanton numbers (n₀=1): 324, 37260, 10792428, 4580482284, 2405245303584, ... ; Common denominator:...

Discriminant

$1-1728z$

Local exponents

$0$ $\frac{ 1}{ 1728}$ $\infty$
$0$ $0$ $\frac{ 1}{ 4}$
$0$ $1$ $\frac{ 1}{ 3}$
$0$ $1$ $\frac{ 2}{ 3}$
$0$ $2$ $\frac{ 3}{ 4}$

\(0\)	\(\frac{ 1}{ 1728}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(0\)	\(1\)	\(\frac{ 1}{ 3}\)
\(0\)	\(1\)	\(\frac{ 2}{ 3}\)
\(0\)	\(2\)	\(\frac{ 3}{ 4}\)

Note:

A-incarnation: X(4,6) in P^5(1,1,1,2,2,3)

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-156\)	\(48\)	\(6\)	\(5\)

3

New Number: 1.12 | AESZ: 12 | Superseeker: 7776 66942277344 | Hash: ad7e2e881b3939396323eb746eb17a58

Degree: 1

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 720, 5821200, 75473798400, 1205906199498000, ...
--> OEIS
Normalized instanton numbers (n₀=1): 7776, 13952088, 66942277344, 475338414733416, 4184555647748620320, ... ; Common denominator:...

Discriminant

$1-27648z$

Local exponents

$0$ $\frac{ 1}{ 27648}$ $\infty$
$0$ $0$ $\frac{ 1}{ 6}$
$0$ $1$ $\frac{ 1}{ 4}$
$0$ $1$ $\frac{ 3}{ 4}$
$0$ $2$ $\frac{ 5}{ 6}$

\(0\)	\(\frac{ 1}{ 27648}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 1}{ 6}\)
\(0\)	\(1\)	\(\frac{ 1}{ 4}\)
\(0\)	\(1\)	\(\frac{ 3}{ 4}\)
\(0\)	\(2\)	\(\frac{ 5}{ 6}\)

Note:

A-incarnation: X(3,4) in P^5(1,1,1,1,1,2)

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-156\)	\(32\)	\(2\)	\(3\)

4

New Number: 1.13 | AESZ: 13 | Superseeker: 67104 28583248229280 | Hash: f833f256db6c016c021add7a2104d2c7

Degree: 1

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 3600, 192099600, 16679709446400, 1791735431214128400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 67104, 847288224, 28583248229280, 1431885139218997920, 88985016340513371957600, ... ; Common denominator:...

Discriminant

$1-186624z$

Local exponents

$0$ $\frac{ 1}{ 186624}$ $\infty$
$0$ $0$ $\frac{ 1}{ 6}$
$0$ $1$ $\frac{ 1}{ 6}$
$0$ $1$ $\frac{ 5}{ 6}$
$0$ $2$ $\frac{ 5}{ 6}$

\(0\)	\(\frac{ 1}{ 186624}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 1}{ 6}\)
\(0\)	\(1\)	\(\frac{ 1}{ 6}\)
\(0\)	\(1\)	\(\frac{ 5}{ 6}\)
\(0\)	\(2\)	\(\frac{ 5}{ 6}\)

Note:

A-incarnation: X(6,6) in P^5(1,1,2,2,3,3)

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-120\)	\(22\)	\(1\)	\(2\)

5

New Number: 1.14 | AESZ: 14 | Superseeker: 1248 683015008 | Hash: 03af56f4ae0cea2c4b219620b08dc49b

Degree: 1

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 240, 498960, 1633632000, 6558930378000, ...
--> OEIS
Normalized instanton numbers (n₀=1): 1248, 597192, 683015008, 1149904141056, 2394928461766560, ... ; Common denominator:...

Discriminant

$1-6912z$

Local exponents

$0$ $\frac{ 1}{ 6912}$ $\infty$
$0$ $0$ $\frac{ 1}{ 6}$
$0$ $1$ $\frac{ 1}{ 2}$
$0$ $1$ $\frac{ 1}{ 2}$
$0$ $2$ $\frac{ 5}{ 6}$

\(0\)	\(\frac{ 1}{ 6912}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 1}{ 6}\)
\(0\)	\(1\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(\frac{ 1}{ 2}\)
\(0\)	\(2\)	\(\frac{ 5}{ 6}\)

Note:

A-incarnation: X(2,6) in P^5(1,1,1,1,1,3)

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-256\)	\(52\)	\(4\)	\(5\)

6

New Number: 1.1 | AESZ: 1 | Superseeker: 575 63441275 | Hash: c86f1c284d8c5119801c6ba1343172bb

Degree: 1

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 120, 113400, 168168000, 305540235000, ...
--> OEIS
Normalized instanton numbers (n₀=1): 575, 121850, 63441275, 48493506000, 45861177777525, ... ; Common denominator:...

Discriminant

$1-3125z$

Local exponents

$0$ $\frac{ 1}{ 3125}$ $\infty$
$0$ $0$ $\frac{ 1}{ 5}$
$0$ $1$ $\frac{ 2}{ 5}$
$0$ $1$ $\frac{ 3}{ 5}$
$0$ $2$ $\frac{ 4}{ 5}$

\(0\)	\(\frac{ 1}{ 3125}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 1}{ 5}\)
\(0\)	\(1\)	\(\frac{ 2}{ 5}\)
\(0\)	\(1\)	\(\frac{ 3}{ 5}\)
\(0\)	\(2\)	\(\frac{ 4}{ 5}\)

Note:

A-incarnation: $X(5) \subset P^4$
B-incarnation: mirror quintic.
P. Candelas, X. de la Ossa, D. Green, L. Parkes,{\em An exactly soluble superconformal theory from a mirror pair of Calabi-Yau manifolds}, Phys. Lett. B 258 (1991), no.1-2, 118-126.

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-200\)	\(50\)	\(5\)	\(5\)

7

New Number: 1.2 | AESZ: 2 | Superseeker: 231200 1700894366474400 | Hash: 709cba5c90462e9488c8a3dbbee8f89c

Degree: 1

$\theta^4-2^{4} 5 x(10\theta+1)(10\theta+3)(10\theta+7)(10\theta+9)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 15120, 3491888400, 1304290155168000, 601680868708529610000, ...
--> OEIS
Normalized instanton numbers (n₀=1): 231200, 12215785600, 1700894366474400, 350154658851324656000, 89338191421813572850115680, ... ; Common denominator:...

Discriminant

$1-800000z$

Local exponents

$0$ $\frac{ 1}{ 800000}$ $\infty$
$0$ $0$ $\frac{ 1}{ 10}$
$0$ $1$ $\frac{ 3}{ 10}$
$0$ $1$ $\frac{ 7}{ 10}$
$0$ $2$ $\frac{ 9}{ 10}$

\(0\)	\(\frac{ 1}{ 800000}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 1}{ 10}\)
\(0\)	\(1\)	\(\frac{ 3}{ 10}\)
\(0\)	\(1\)	\(\frac{ 7}{ 10}\)
\(0\)	\(2\)	\(\frac{ 9}{ 10}\)

Note:

A-incarnation: X(10) in P^4(1,1,1,2,5)

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-288\)	\(34\)	\(1\)	\(3\)

8

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.

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-128\)	\(64\)	\(16\)	\(8\)

9

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	,...

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

10

New Number: 1.5 | AESZ: 5 | Superseeker: 60 134292 | Hash: a6c4fb927cb2a4bb1103c1c739a252b0

Degree: 1

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 24, 3240, 672000, 169785000, ...
--> OEIS
Normalized instanton numbers (n₀=1): 60, 1869, 134292, 14016600, 1806410976, ... ; Common denominator:...

Discriminant

$1-432z$

Local exponents

$0$ $\frac{ 1}{ 432}$ $\infty$
$0$ $0$ $\frac{ 1}{ 3}$
$0$ $1$ $\frac{ 1}{ 2}$
$0$ $1$ $\frac{ 1}{ 2}$
$0$ $2$ $\frac{ 2}{ 3}$

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

Note:

A-incarnation: X(2,2,3) in $P^6$.

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-144\)	\(60\)	\(12\)	\(7\)

11

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 $P^5$.

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-176\)	\(56\)	\(8\)	\(6\)

12

New Number: 1.7 | AESZ: 7 | Superseeker: 14752 711860273440 | Hash: b899892fb606c7eeb86a2cc55f92d6f2

Degree: 1

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 1680, 32432400, 999456057600, 37905932634570000, ...
--> OEIS
Normalized instanton numbers (n₀=1): 14752, 64417456, 711860273440, 11596528012396656, 233938237312624658400, ... ; Common denominator:...

Discriminant

$1-65536z$

Local exponents

$0$ $\frac{ 1}{ 65536}$ $\infty$
$0$ $0$ $\frac{ 1}{ 8}$
$0$ $1$ $\frac{ 3}{ 8}$
$0$ $1$ $\frac{ 5}{ 8}$
$0$ $2$ $\frac{ 7}{ 8}$

\(0\)	\(\frac{ 1}{ 65536}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 1}{ 8}\)
\(0\)	\(1\)	\(\frac{ 3}{ 8}\)
\(0\)	\(1\)	\(\frac{ 5}{ 8}\)
\(0\)	\(2\)	\(\frac{ 7}{ 8}\)

Note:

A-incarnation: X(8) in P^4(1,1,1,1,4)

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-296\)	\(44\)	\(2\)	\(4\)

13

New Number: 1.8 | AESZ: 8 | Superseeker: 2628 3966805740 | Hash: 1a7187fdf63fe8761c969fdab1af1c36

Degree: 1

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 360, 1247400, 6861254400, 46381007673000, ...
--> OEIS
Normalized instanton numbers (n₀=1): 2628, 2009484, 3966805740, 11533584001896, 41531678111043360, ... ; Common denominator:...

Discriminant

$1-11664z$

Local exponents

$0$ $\frac{ 1}{ 11664}$ $\infty$
$0$ $0$ $\frac{ 1}{ 6}$
$0$ $1$ $\frac{ 1}{ 3}$
$0$ $1$ $\frac{ 2}{ 3}$
$0$ $2$ $\frac{ 5}{ 6}$

\(0\)	\(\frac{ 1}{ 11664}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 1}{ 6}\)
\(0\)	\(1\)	\(\frac{ 1}{ 3}\)
\(0\)	\(1\)	\(\frac{ 2}{ 3}\)
\(0\)	\(2\)	\(\frac{ 5}{ 6}\)

Note:

A-incarnation of $X(6) \subset P^4(1,1,1,1,2)$.

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-204\)	\(42\)	\(3\)	\(4\)

14

New Number: 1.9 | AESZ: 9 | Superseeker: 678816 69080128815414048 | Hash: 33dd5470a0dc987468fcd11c1de8ee11

Degree: 1

$\theta^4-2^{4} 3^{2} x(12\theta+1)(12\theta+5)(12\theta+7)(12\theta+11)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 55440, 48188059920, 67388324683680000, 116214168909224876490000, ...
--> OEIS
Normalized instanton numbers (n₀=1): 678816, 137685060720, 69080128815414048, 51172489466251340674608, 46928387692914781844159094240, ... ; Common denominator:...

Discriminant

$1-2985984z$

Local exponents

$0$ $\frac{ 1}{ 2985984}$ $\infty$
$0$ $0$ $\frac{ 1}{ 12}$
$0$ $1$ $\frac{ 5}{ 12}$
$0$ $1$ $\frac{ 7}{ 12}$
$0$ $2$ $\frac{ 11}{ 12}$

\(0\)	\(\frac{ 1}{ 2985984}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 1}{ 12}\)
\(0\)	\(1\)	\(\frac{ 5}{ 12}\)
\(0\)	\(1\)	\(\frac{ 7}{ 12}\)
\(0\)	\(2\)	\(\frac{ 11}{ 12}\)

Note:

A-incarnation: X(2,12) in P^5(1,1,1,1,4,6)

Calabi-Yau differential operator database v.3

Summary

Discriminant

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:

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: