Calabi-Yau differential operator database v.3.0

1

New Number: 3.13 | AESZ: | Superseeker: 352 15001120/3 | Hash: b5a6f76d274395537de2c3169fdac9bf

Degree: 3

$\theta^4-2^{2} x\left(688\theta^4+1232\theta^3+902\theta^2+286\theta+33\right)+2^{4} 3^{2} x^{2}(4\theta+3)(3776\theta^3+10096\theta^2+8268\theta+1515)-2^{10} 3^{4} 5^{2} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 132, 62748, 43686384, 37830871260, ...
--> OEIS
Normalized instanton numbers (n₀=1): 352, 18676, 15001120/3, 1489325052, 586526654304, ... ; Common denominator:...

Discriminant

$-(1600z-1)(-1+576z)^2$

Local exponents

$0$ $\frac{ 1}{ 1600}$ $\frac{ 1}{ 576}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$0$ $1$ $\frac{ 1}{ 2}$ $\frac{ 3}{ 4}$
$0$ $1$ $1$ $\frac{ 7}{ 4}$
$0$ $2$ $\frac{ 3}{ 2}$ $\frac{ 9}{ 4}$

\(0\)	\(\frac{ 1}{ 1600}\)	\(\frac{ 1}{ 576}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(0\)	\(1\)	\(\frac{ 1}{ 2}\)	\(\frac{ 3}{ 4}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 7}{ 4}\)
\(0\)	\(2\)	\(\frac{ 3}{ 2}\)	\(\frac{ 9}{ 4}\)

Note:

Operator equivalent to AESZ 229

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-56\)	\(36\)	\(6\)	\(4\)

2

New Number: 3.14 | AESZ: | Superseeker: 444 19050964 | Hash: dc96aa2da269d989ee90c49dab6a9c5a

Degree: 3

$\theta^4-2^{2} x\left(452\theta^4+920\theta^3+633\theta^2+173\theta+17\right)-2^{4} x^{2}(4\theta+3)(3808\theta^3+10504\theta^2+8884\theta+1635)-2^{8} 11^{2} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 68, 42220, 38866320, 43812369900, ...
--> OEIS
Normalized instanton numbers (n₀=1): 444, 57104, 19050964, 9432910668, 5781274591408, ... ; Common denominator:...

Discriminant

$-(1936z-1)(1+64z)^2$

Local exponents

$-\frac{ 1}{ 64}$ $0$ $\frac{ 1}{ 1936}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$\frac{ 1}{ 2}$ $0$ $1$ $\frac{ 3}{ 4}$
$1$ $0$ $1$ $\frac{ 7}{ 4}$
$\frac{ 3}{ 2}$ $0$ $2$ $\frac{ 9}{ 4}$

\(-\frac{ 1}{ 64}\)	\(0\)	\(\frac{ 1}{ 1936}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(\frac{ 1}{ 2}\)	\(0\)	\(1\)	\(\frac{ 3}{ 4}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 7}{ 4}\)
\(\frac{ 3}{ 2}\)	\(0\)	\(2\)	\(\frac{ 9}{ 4}\)

Note:

This is operator Pi = 3.14 (approx.), equivalent to AESZ 238.

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-100\)	\(38\)	\(5\)	\(4\)

3

New Number: 3.17 | AESZ: 387 | Superseeker: 68 125636/3 | Hash: 06864aab02693f4b84eb494138bb3428

Degree: 3

$\theta^4-2^{2} x\left(228\theta^4+456\theta^3+385\theta^2+157\theta+26\right)+2^{11} x^{2}(\theta+1)^2(132\theta^2+264\theta+109)-2^{18} 5^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 104, 18600, 3925760, 906368680, ...
--> OEIS
Normalized instanton numbers (n₀=1): 68, 204, 125636/3, 841384, 123715360, ... ; Common denominator:...

Discriminant

$-(400z-1)(-1+256z)^2$

Local exponents

$0$ $\frac{ 1}{ 400}$ $\frac{ 1}{ 256}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $0$ $1$
$0$ $1$ $1$ $2$
$0$ $2$ $1$ $\frac{ 5}{ 2}$

\(0\)	\(\frac{ 1}{ 400}\)	\(\frac{ 1}{ 256}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(0\)	\(1\)
\(0\)	\(1\)	\(1\)	\(2\)
\(0\)	\(2\)	\(1\)	\(\frac{ 5}{ 2}\)

Note:

This is operator "3.17" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(80\)	\(24\)	\(12\)	\(4\)

4

New Number: 3.18 | AESZ: 388 | Superseeker: 266 11433160/3 | Hash: 7e11db69c1b7bd8781e54a5eadb0e307

Degree: 3

$\theta^4-2 x\left(582\theta^4+1164\theta^3+815\theta^2+233\theta+25\right)+2^{2} x^{2}(\theta+1)^2(2316\theta^2+4632\theta+1907)-2^{4} 17^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 50, 17142, 9383540, 6301530550, ...
--> OEIS
Normalized instanton numbers (n₀=1): 266, 19320, 11433160/3, 1106069392, 397606861972, ... ; Common denominator:...

Discriminant

$-(1156z-1)(4z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 1156}$ $\frac{ 1}{ 4}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $0$ $1$
$0$ $1$ $1$ $2$
$0$ $2$ $1$ $\frac{ 5}{ 2}$

\(0\)	\(\frac{ 1}{ 1156}\)	\(\frac{ 1}{ 4}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(0\)	\(1\)
\(0\)	\(1\)	\(1\)	\(2\)
\(0\)	\(2\)	\(1\)	\(\frac{ 5}{ 2}\)

Note:

This is operator "3.18" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-64\)	\(36\)	\(6\)	\(4\)

5

New Number: 3.22 | AESZ: 392 | Superseeker: 166 1016100 | Hash: 5862be5cc4d3ec1686e6b9a6ec08f7e7

Degree: 3

$\theta^4-2 x\left(230\theta^4+496\theta^3+323\theta^2+75\theta+6\right)-2^{2} 3 x^{2}(6\theta+5)(1866\theta^3+5341\theta^2+4760\theta+1084)-2^{4} 3^{2} 13^{2} x^{3}(6\theta+5)(6\theta+11)(3\theta+1)(3\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 12, 5760, 1664544, 681014880, ...
--> OEIS
Normalized instanton numbers (n₀=1): 166, 8076, 1016100, 189329096, 43879949258, ... ; Common denominator:...

Discriminant

$-(676z-1)(1+108z)^2$

Local exponents

$-\frac{ 1}{ 108}$ $0$ $\frac{ 1}{ 676}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 3}$
$\frac{ 1}{ 3}$ $0$ $1$ $\frac{ 5}{ 6}$
$1$ $0$ $1$ $\frac{ 11}{ 6}$
$\frac{ 4}{ 3}$ $0$ $2$ $\frac{ 7}{ 3}$

\(-\frac{ 1}{ 108}\)	\(0\)	\(\frac{ 1}{ 676}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 3}\)
\(\frac{ 1}{ 3}\)	\(0\)	\(1\)	\(\frac{ 5}{ 6}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 11}{ 6}\)
\(\frac{ 4}{ 3}\)	\(0\)	\(2\)	\(\frac{ 7}{ 3}\)

Note:

This is operator "3.22" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-36\)	\(34\)	\(7\)	\(4\)

6

New Number: 3.21 | AESZ: 391 | Superseeker: 964 85888580/3 | Hash: 907f1fbd0b6f7c89689fb136ee18482a

Degree: 3

$\theta^4-2^{2} x\left(3460\theta^4+5768\theta^3+4385\theta^2+1501\theta+186\right)+2^{10} 3^{2} x^{2}(4\theta+3)(1732\theta^3+4475\theta^2+3531\theta+645)-2^{14} 3^{4} 17^{2} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 744, 1731240, 5192436480, 17479541356200, ...
--> OEIS
Normalized instanton numbers (n₀=1): 964, -111140, 85888580/3, -9197858184, 3544241969952, ... ; Common denominator:...

Discriminant

$-(4624z-1)(-1+4608z)^2$

Local exponents

$0$ $\frac{ 1}{ 4624}$ $\frac{ 1}{ 4608}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$0$ $1$ $\frac{ 1}{ 2}$ $\frac{ 3}{ 4}$
$0$ $1$ $1$ $\frac{ 7}{ 4}$
$0$ $2$ $\frac{ 3}{ 2}$ $\frac{ 9}{ 4}$

\(0\)	\(\frac{ 1}{ 4624}\)	\(\frac{ 1}{ 4608}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(0\)	\(1\)	\(\frac{ 1}{ 2}\)	\(\frac{ 3}{ 4}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 7}{ 4}\)
\(0\)	\(2\)	\(\frac{ 3}{ 2}\)	\(\frac{ 9}{ 4}\)

Note:

This is operator "3.21" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(304\)	\(24\)	\(12\)	\(4\)

7

New Number: 3.6 | AESZ: ~33 | Superseeker: 196 2993772 | Hash: 29aeacb8c7e91c8c2838e65ce2750b5a

Degree: 3

$\theta^4+2^{2} x\left(60\theta^4-8\theta^3+31\theta^2+35\theta+6\right)-2^{10} x^{2}(4\theta+3)(132\theta^3+395\theta^2+363\theta+69)-2^{14} 7^{2} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)$

Maple LaTex

Coefficients of the holomorphic solution: 1, -24, 13992, -920832, 1808021160, ...
--> OEIS
Normalized instanton numbers (n₀=1): 196, 17212, 2993772, 789858520, 260782261024, ... ; Common denominator:...

Discriminant

$-(784z-1)(1+512z)^2$

Local exponents

$-\frac{ 1}{ 512}$ $0$ $\frac{ 1}{ 784}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$\frac{ 1}{ 2}$ $0$ $1$ $\frac{ 3}{ 4}$
$1$ $0$ $1$ $\frac{ 7}{ 4}$
$\frac{ 3}{ 2}$ $0$ $2$ $\frac{ 9}{ 4}$

\(-\frac{ 1}{ 512}\)	\(0\)	\(\frac{ 1}{ 784}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(\frac{ 1}{ 2}\)	\(0\)	\(1\)	\(\frac{ 3}{ 4}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 7}{ 4}\)
\(\frac{ 3}{ 2}\)	\(0\)	\(2\)	\(\frac{ 9}{ 4}\)

Note:

Operator AESZ 33 is replaced by this equivalent operator.

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-72\)	\(36\)	\(6\)	\(4\)

8

New Number: 3.7 | AESZ: ~73 | Superseeker: 90 151648 | Hash: 9f672e1168859bdcc8ddc7a201c57968

Degree: 3

$\theta^4-2 3^{2} x\left(6\theta^4+12\theta^3+3\theta^2-3\theta-1\right)-2^{2} 3^{6} x^{2}(\theta+1)^2(20\theta^2+40\theta+17)-2^{4} 3^{10} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, -18, 2754, 37620, 43789410, ...
--> OEIS
Normalized instanton numbers (n₀=1): 90, 2196, 151648, 14813388, 1820806056, ... ; Common denominator:...

Discriminant

$-(324z-1)(1+108z)^2$

Local exponents

$-\frac{ 1}{ 108}$ $0$ $\frac{ 1}{ 324}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $0$ $1$ $1$
$1$ $0$ $1$ $2$
$1$ $0$ $2$ $\frac{ 5}{ 2}$

\(-\frac{ 1}{ 108}\)	\(0\)	\(\frac{ 1}{ 324}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(0\)	\(1\)	\(1\)
\(1\)	\(0\)	\(1\)	\(2\)
\(1\)	\(0\)	\(2\)	\(\frac{ 5}{ 2}\)

Note:

Operator equivalent to AESZ 73

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(12\)	\(30\)	\(9\)	\(4\)

9

New Number: 4.41 | AESZ: 220 | Superseeker: 128 382592 | Hash: 671a1aa788ead53985e13ad6774d0189

Degree: 4

$\theta^4-2^{4} x\left(20\theta^4+56\theta^3+38\theta^2+10\theta+1\right)-2^{10} x^{2}\left(84\theta^4+240\theta^3+261\theta^2+134\theta+25\right)-2^{16} x^{3}(2\theta+1)^2(23\theta^2+55\theta+39)-2^{23} x^{4}(2\theta+1)^2(2\theta+3)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 16, 3600, 851200, 257328400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 128, 4084, 382592, 51510860, 8644861312, ... ; Common denominator:...

Discriminant

$-(512z-1)(64z+1)^3$

Local exponents

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

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

Note:

Sporadic Operator.
Reducible to 3.32, so not a primary operator.
B-Incarnation: 81111- x 82--11

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-8\)	\(32\)	\(8\)	\(4\)

10

New Number: 4.52 | AESZ: 258 | Superseeker: 480 4215904 | Hash: bfb9f01124fd9980817cbf1b50f789c3

Degree: 4

$\theta^4-2^{4} x\left(16\theta^4+224\theta^3+156\theta^2+44\theta+5\right)-2^{14} x^{2}\left(48\theta^4+48\theta^3-120\theta^2-66\theta-11\right)-2^{22} x^{3}\left(16\theta^4-192\theta^3-156\theta^2-48\theta-5\right)+2^{32} x^{4}\left((2\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 80, 24336, 11398400, 6632189200, ...
--> OEIS
Normalized instanton numbers (n₀=1): 480, -16536, 4215904, -242723592, 151800032928, ... ; Common denominator:...

Discriminant

$(1024z-1)(256z-1)(1+512z)^2$

Local exponents

$-\frac{ 1}{ 512}$ $0$ $\frac{ 1}{ 1024}$ $\frac{ 1}{ 256}$ $\infty$
$0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $1$ $\frac{ 1}{ 2}$
$3$ $0$ $1$ $1$ $\frac{ 1}{ 2}$
$4$ $0$ $2$ $2$ $\frac{ 1}{ 2}$

\(-\frac{ 1}{ 512}\)	\(0\)	\(\frac{ 1}{ 1024}\)	\(\frac{ 1}{ 256}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(0\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)
\(3\)	\(0\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)
\(4\)	\(0\)	\(2\)	\(2\)	\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator.

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(48\)	\(32\)	\(8\)	\(4\)

11

New Number: 5.13 | AESZ: 83 | Superseeker: -80 -174096 | Hash: 171e1251d8e4f7de878d0d07de6f58ab

Degree: 5

$\theta^4-2^{4} x\left(88\theta^4+32\theta^3+33\theta^2+17\theta+3\right)+2^{9} x^{2}\left(1504\theta^4+1408\theta^3+1436\theta^2+596\theta+93\right)-2^{18} x^{3}\left(776\theta^4+1344\theta^3+1381\theta^2+651\theta+117\right)+2^{23} 3 x^{4}(2\theta+1)(512\theta^3+1152\theta^2+1054\theta+339)-2^{31} 3^{2} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 48, 5328, 779520, 131619600, ...
--> OEIS
Normalized instanton numbers (n₀=1): -80, -2954, -174096, -13270953, -1179175536, ... ; Common denominator:...

Discriminant

$-(128z-1)(384z-1)^2(256z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 384}$ $\frac{ 1}{ 256}$ $\frac{ 1}{ 128}$ $\infty$
$0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $\frac{ 1}{ 2}$ $1$ $\frac{ 3}{ 4}$
$0$ $3$ $\frac{ 1}{ 2}$ $1$ $\frac{ 5}{ 4}$
$0$ $4$ $1$ $2$ $\frac{ 3}{ 2}$

\(0\)	\(\frac{ 1}{ 384}\)	\(\frac{ 1}{ 256}\)	\(\frac{ 1}{ 128}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(\frac{ 1}{ 2}\)	\(1\)	\(\frac{ 3}{ 4}\)
\(0\)	\(3\)	\(\frac{ 1}{ 2}\)	\(1\)	\(\frac{ 5}{ 4}\)
\(0\)	\(4\)	\(1\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.13" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(360\)	\(-16\)	\(32\)	\(4\)

12

New Number: 5.75 | AESZ: 298 | Superseeker: 205/9 97622/9 | Hash: e52d50673ec5c795512e2bc3e1017b12

Degree: 5

$3^{4} \theta^4-3^{2} x\left(1993\theta^4+3218\theta^3+2437\theta^2+828\theta+108\right)+2^{5} x^{2}\left(17486\theta^4+25184\theta^3+12239\theta^2+2790\theta+297\right)-2^{8} x^{3}\left(23620\theta^4+34776\theta^3+28905\theta^2+12447\theta+2106\right)+2^{15} x^{4}(2\theta+1)(340\theta^3+618\theta^2+455\theta+129)-2^{22} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 12, 708, 63840, 6989220, ...
--> OEIS
Normalized instanton numbers (n₀=1): 205/9, 3206/9, 97622/9, 496806, 254037095/9, ... ; Common denominator:...

Discriminant

$-(z-1)(1024z^2-192z+1)(-9+128z)^2$

Local exponents

$0$ $\frac{ 3}{ 32}-\frac{ 1}{ 16}\sqrt{ 2}$ $\frac{ 9}{ 128}$ $\frac{ 3}{ 32}+\frac{ 1}{ 16}\sqrt{ 2}$ $1$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $1$ $1$ $1$
$0$ $1$ $3$ $1$ $1$ $1$
$0$ $2$ $4$ $2$ $2$ $\frac{ 3}{ 2}$

\(0\)	\(\frac{ 3}{ 32}-\frac{ 1}{ 16}\sqrt{ 2}\)	\(\frac{ 9}{ 128}\)	\(\frac{ 3}{ 32}+\frac{ 1}{ 16}\sqrt{ 2}\)	\(1\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(3\)	\(1\)	\(1\)	\(1\)
\(0\)	\(2\)	\(4\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.75" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-92\)	\(12\)	\(18\)	\(4\)

13

New Number: 5.90 | AESZ: 330 | Superseeker: 352 3284448 | Hash: ba5b66d5fe92237e6416a117563571e9

Degree: 5

$\theta^4+2^{4} x\left(112\theta^4-64\theta^3-32\theta^2+1\right)+2^{14} x^{2}\left(56\theta^4-64\theta^3+3\theta^2-10\theta-4\right)+2^{20} x^{3}\left(32\theta^4-384\theta^3-436\theta^2-264\theta-55\right)-2^{29} 3 x^{4}(2\theta+1)(10\theta+7)(2\theta^2+4\theta+3)-2^{38} 3^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, -16, 4368, -344320, 107445520, ...
--> OEIS
Normalized instanton numbers (n₀=1): 352, -23368, 3284448, -578330224, 120252731680, ... ; Common denominator:...

Discriminant

$-(-1+256z)(256z+1)^2(768z+1)^2$

Local exponents

$-\frac{ 1}{ 256}$ $-\frac{ 1}{ 768}$ $0$ $\frac{ 1}{ 256}$ $\infty$
$0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$\frac{ 1}{ 2}$ $1$ $0$ $1$ $1$
$\frac{ 1}{ 2}$ $3$ $0$ $1$ $1$
$1$ $4$ $0$ $2$ $\frac{ 3}{ 2}$

\(-\frac{ 1}{ 256}\)	\(-\frac{ 1}{ 768}\)	\(0\)	\(\frac{ 1}{ 256}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(\frac{ 1}{ 2}\)	\(1\)	\(0\)	\(1\)	\(1\)
\(\frac{ 1}{ 2}\)	\(3\)	\(0\)	\(1\)	\(1\)
\(1\)	\(4\)	\(0\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

B-Incarnation as double octic D.O.20

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(320\)	\(16\)	\(16\)	\(4\)

14

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

Degree: 1

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

Maple LaTex

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	,...

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

15

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	,...

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

16

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 $X(6) \subset P^4(1,1,1,1,2)$.

17

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

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

Note:

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

\(-56\lambda\)	\(\frac{ 5}{ 2}\)	\(1\)	\(1\)
\(-\frac{ 3}{ 2}\)	\(-3\)	\(-1\)	\(0\)
\(0\)	\(6\)	\(0\)	\(0\)
\(-6\)	\(0\)	\(0\)	\(0\)

\(-100\lambda\)	\(\frac{ 29}{ 12}\)	\(1\)	\(1\)
\(-\frac{ 19}{ 12}\)	\(-\frac{ 5}{ 2}\)	\(-1\)	\(0\)
\(0\)	\(5\)	\(0\)	\(0\)
\(-5\)	\(0\)	\(0\)	\(0\)

\(80\lambda\)	\(3\)	\(1\)	\(1\)
\(-1\)	\(-6\)	\(-1\)	\(0\)
\(0\)	\(12\)	\(0\)	\(0\)
\(-12\)	\(0\)	\(0\)	\(0\)

\(-64\lambda\)	\(\frac{ 5}{ 2}\)	\(1\)	\(1\)
\(-\frac{ 3}{ 2}\)	\(-3\)	\(-1\)	\(0\)
\(0\)	\(6\)	\(0\)	\(0\)
\(-6\)	\(0\)	\(0\)	\(0\)

\(-36\lambda\)	\(\frac{ 31}{ 12}\)	\(1\)	\(1\)
\(-\frac{ 17}{ 12}\)	\(-\frac{ 7}{ 2}\)	\(-1\)	\(0\)
\(0\)	\(7\)	\(0\)	\(0\)
\(-7\)	\(0\)	\(0\)	\(0\)

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

Calabi-Yau differential operator database v.3

Summary

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:

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