Calabi-Yau differential operator database v.3.0

1

New Number: 2.47 | AESZ: | Superseeker: -3488 -1142687008 | Hash: 413005461e43cfa75125577c2d4c2fde

Degree: 2

$\theta^4-2^{4} x\left(2048\theta^4+4096\theta^3+4800\theta^2+2752\theta+599\right)+2^{24} x^{2}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 9584, 121274640, 1675847866112, 24182028281658640, ...
--> OEIS
Normalized instanton numbers (n₀=1): -3488, -1406056, -1142687008, -1211614451216, -1500013956719584, ... ; Common denominator:...

Discriminant

$(16384z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 16384}$ $\infty$
$0$ $0$ $\frac{ 3}{ 4}$
$0$ $-\frac{ 1}{ 2}$ $1$
$0$ $1$ $1$
$0$ $\frac{ 3}{ 2}$ $\frac{ 5}{ 4}$

\(0\)	\(\frac{ 1}{ 16384}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 3}{ 4}\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(1\)
\(0\)	\(1\)	\(1\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 5}{ 4}\)

Note:

Operator equivalent to $\hat{10}$

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

2

New Number: 2.62 | AESZ: 28 | Superseeker: 5 312 | Hash: 06dd455cafc5097e4f671d385984c1a2

Degree: 2

$\theta^4-x\left(65\theta^4+130\theta^3+105\theta^2+40\theta+6\right)+2^{2} x^{2}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 6, 126, 3948, 149310, ...
--> OEIS
Normalized instanton numbers (n₀=1): 5, 28, 312, 4808, 91048, ... ; Common denominator:...

Discriminant

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

Local exponents

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

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

Note:

A-incarnation: $X(1, 1, 1, 1, 1, 1) \subset Grass(3, 6)$

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-96\)	\(84\)	\(42\)	\(14\)

3

New Number: 2.63 | AESZ: 84 | Superseeker: -4 -44 | Hash: 908b978c0c447d3643c3018c40e7f5d1

Degree: 2

$\theta^4-2^{2} x\left(32\theta^4+64\theta^3+63\theta^2+31\theta+6\right)+2^{8} x^{2}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 24, 936, 43008, 2145960, ...
--> OEIS
Normalized instanton numbers (n₀=1): -4, -11, -44, -156, -288, ... ; Common denominator:...

Discriminant

$(64z-1)^2$

Local exponents

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

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

Note:

This is operator "2.63" from ...

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

4

New Number: 5.102 | AESZ: 352 | Superseeker: 1 -12 | Hash: fc8b141522720827b1dd2cd28a232c1b

Degree: 5

$\theta^4-x\left(70\theta^4+86\theta^3+77\theta^2+34\theta+6\right)+3 x^{2}\left(675\theta^4+1602\theta^3+1933\theta^2+1130\theta+258\right)-2^{2} 3^{3} x^{3}\left(271\theta^4+888\theta^3+1259\theta^2+831\theta+207\right)+2^{2} 3^{5} x^{4}\left(212\theta^4+808\theta^3+1189\theta^2+773\theta+186\right)-2^{4} 3^{7} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 6, 54, 492, 3510, ...
--> OEIS
Normalized instanton numbers (n₀=1): 1, -7/8, -12, -131/4, 90, ... ; Common denominator:...

Discriminant

$-(16z-1)(432z^2-36z+1)(-1+9z)^2$

Local exponents

$0$ $\infty$ $\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I$ $\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I$ $\frac{ 1}{ 16}$ $\frac{ 1}{ 9}$
$0$ $\frac{ 3}{ 4}$ $0$ $0$ $0$ $0$
$0$ $1$ $1$ $1$ $1$ $1$
$0$ $1$ $1$ $1$ $1$ $3$
$0$ $\frac{ 5}{ 4}$ $2$ $2$ $2$ $4$

\(0\)	\(\infty\)	\(\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I\)	\(\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I\)	\(\frac{ 1}{ 16}\)	\(\frac{ 1}{ 9}\)
\(0\)	\(\frac{ 3}{ 4}\)	\(0\)	\(0\)	\(0\)	\(0\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(3\)
\(0\)	\(\frac{ 5}{ 4}\)	\(2\)	\(2\)	\(2\)	\(4\)

Note:

This is operator "5.102" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-216\)	\(216\)	\(288\)	\(66\)

5

New Number: 5.112 | AESZ: 395 | Superseeker: 4 940 | Hash: 2d13c01eaf16983977dfb0325c5f376e

Degree: 5

$\theta^4-2^{2} x\theta(22\theta^3+8\theta^2+5\theta+1)+2^{5} x^{2}\left(34\theta^4-152\theta^3-265\theta^2-163\theta-36\right)+2^{8} x^{3}\left(142\theta^4+600\theta^3+335\theta^2-39\theta-54\right)-2^{11} 3 x^{4}\left(68\theta^4-56\theta^3-295\theta^2-261\theta-72\right)-2^{15} 3^{2} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 0, 72, 1728, 72360, ...
--> OEIS
Normalized instanton numbers (n₀=1): 4, 60, 940, 19091, 463904, ... ; Common denominator:...

Discriminant

$-(16z+1)(8z+1)(64z-1)(-1+24z)^2$

Local exponents

$0$ $-\frac{ 1}{ 16}$ $\frac{ 1}{ 24}$ $\infty$ $\frac{ 1}{ 64}$ $-\frac{ 1}{ 8}$
$0$ $0$ $0$ $\frac{ 3}{ 4}$ $0$ $0$
$0$ $1$ $1$ $1$ $1$ $1$
$0$ $1$ $3$ $1$ $1$ $1$
$0$ $2$ $4$ $\frac{ 5}{ 4}$ $2$ $2$

\(0\)	\(-\frac{ 1}{ 16}\)	\(\frac{ 1}{ 24}\)	\(\infty\)	\(\frac{ 1}{ 64}\)	\(-\frac{ 1}{ 8}\)
\(0\)	\(0\)	\(0\)	\(\frac{ 3}{ 4}\)	\(0\)	\(0\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(3\)	\(1\)	\(1\)	\(1\)
\(0\)	\(2\)	\(4\)	\(\frac{ 5}{ 4}\)	\(2\)	\(2\)

Note:

This is operator "5.112" from ...

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

6

New Number: 5.49 | AESZ: 248 | Superseeker: 7/3 148 | Hash: 0c9ccff1cb4f5096e455a9026799ed5a

Degree: 5

$3^{2} \theta^4-3 x\left(106\theta^4+146\theta^3+115\theta^2+42\theta+6\right)-x^{2}\left(4511\theta^4+24314\theta^3+37829\theta^2+23598\theta+5286\right)+2^{2} x^{3}\left(10457\theta^4+32184\theta^3+24449\theta^2+3627\theta-1317\right)-2^{2} 11 x^{4}\left(1596\theta^4+2040\theta^3-101\theta^2-1085\theta-386\right)-2^{4} 11^{2} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 2, 54, 1028, 29110, ...
--> OEIS
Normalized instanton numbers (n₀=1): 7/3, 551/24, 148, 8241/4, 86854/3, ... ; Common denominator:...

Discriminant

$-(16z+1)(16z^2+44z-1)(-3+11z)^2$

Local exponents

$0$ $-\frac{ 11}{ 8}+\frac{ 5}{ 8}\sqrt{ 5}$ $\infty$ $-\frac{ 1}{ 16}$ $\frac{ 3}{ 11}$ $-\frac{ 11}{ 8}-\frac{ 5}{ 8}\sqrt{ 5}$
$0$ $0$ $\frac{ 3}{ 4}$ $0$ $0$ $0$
$0$ $1$ $1$ $1$ $1$ $1$
$0$ $1$ $1$ $1$ $3$ $1$
$0$ $2$ $\frac{ 5}{ 4}$ $2$ $4$ $2$

\(0\)	\(-\frac{ 11}{ 8}+\frac{ 5}{ 8}\sqrt{ 5}\)	\(\infty\)	\(-\frac{ 1}{ 16}\)	\(\frac{ 3}{ 11}\)	\(-\frac{ 11}{ 8}-\frac{ 5}{ 8}\sqrt{ 5}\)
\(0\)	\(0\)	\(\frac{ 3}{ 4}\)	\(0\)	\(0\)	\(0\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)	\(3\)	\(1\)
\(0\)	\(2\)	\(\frac{ 5}{ 4}\)	\(2\)	\(4\)	\(2\)

Note:

This is operator "5.49" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-92\)	\(84\)	\(48\)	\(15\)

7

New Number: 5.51 | AESZ: 250 | Superseeker: 308/23 70799/23 | Hash: 9c19794a84073d1c6dfd11c8a7c9a740

Degree: 5

$23^{2} \theta^4-23 x\left(3271\theta^4+5078\theta^3+3896\theta^2+1357\theta+184\right)+x^{2}\left(1357863\theta^4+999924\theta^3-787393\theta^2-850862\theta-205712\right)-2^{3} x^{3}\left(775799\theta^4-272481\theta^3-218821\theta^2+176709\theta+100234\right)-2^{4} 61 x^{4}\left(1005\theta^4-15654\theta^3-36317\theta^2-27938\theta-7304\right)-2^{9} 61^{2} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 324, 19304, 1388260, ...
--> OEIS
Normalized instanton numbers (n₀=1): 308/23, 3526/23, 70799/23, 2148684/23, 81402822/23, ... ; Common denominator:...

Discriminant

$-(512z^3+113z^2+121z-1)(-23+244z)^2$

Local exponents

$0$ ≈$-0.114451+0.474453I$ ≈$0.008199$ $\infty$ ≈$-0.114451-0.474453I$ $\frac{ 23}{ 244}$
$0$ $0$ $0$ $\frac{ 3}{ 4}$ $0$ $0$
$0$ $1$ $1$ $1$ $1$ $1$
$0$ $1$ $1$ $1$ $1$ $3$
$0$ $2$ $2$ $\frac{ 5}{ 4}$ $2$ $4$

\(0\)	≈\(-0.114451+0.474453I\)	≈\(0.008199\)	\(\infty\)	≈\(-0.114451-0.474453I\)	\(\frac{ 23}{ 244}\)
\(0\)	\(0\)	\(0\)	\(\frac{ 3}{ 4}\)	\(0\)	\(0\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(3\)
\(0\)	\(2\)	\(2\)	\(\frac{ 5}{ 4}\)	\(2\)	\(4\)

Note:

This is operator "5.51" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-74\)	\(62\)	\(23\)	\(9\)

8

New Number: 5.79 | AESZ: 310 | Superseeker: 181/11 47171/11 | Hash: 2b9b103b1c8f0d3175cd1fb9ef5aacc2

Degree: 5

$11^{2} \theta^4-11 x\left(1673\theta^4+3046\theta^3+2337\theta^2+814\theta+110\right)+2 5 x^{2}\left(19247\theta^4+28298\theta^3+13285\theta^2+3454\theta+660\right)-2^{2} x^{3}\left(167497\theta^4+245982\theta^3+227451\theta^2+115434\theta+22968\right)+2^{3} 5^{2} x^{4}\left(4079\theta^4+10270\theta^3+11427\theta^2+6226\theta+1340\right)-2^{5} 5^{4} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 10, 450, 30772, 2551810, ...
--> OEIS
Normalized instanton numbers (n₀=1): 181/11, 2018/11, 47171/11, 3261479/22, 69313270/11, ... ; Common denominator:...

Discriminant

$-(z-1)(128z^2-142z+1)(-11+50z)^2$

Local exponents

$0$ $1$ $\infty$ $\frac{ 71}{ 128}-\frac{ 17}{ 128}\sqrt{ 17}$ $\frac{ 71}{ 128}+\frac{ 17}{ 128}\sqrt{ 17}$ $\frac{ 11}{ 50}$
$0$ $0$ $\frac{ 3}{ 4}$ $0$ $0$ $0$
$0$ $1$ $1$ $1$ $1$ $1$
$0$ $1$ $1$ $1$ $1$ $3$
$0$ $2$ $\frac{ 5}{ 4}$ $2$ $2$ $4$

\(0\)	\(1\)	\(\infty\)	\(\frac{ 71}{ 128}-\frac{ 17}{ 128}\sqrt{ 17}\)	\(\frac{ 71}{ 128}+\frac{ 17}{ 128}\sqrt{ 17}\)	\(\frac{ 11}{ 50}\)
\(0\)	\(0\)	\(\frac{ 3}{ 4}\)	\(0\)	\(0\)	\(0\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(3\)
\(0\)	\(2\)	\(\frac{ 5}{ 4}\)	\(2\)	\(2\)	\(4\)

Note:

This is operator "5.79" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-516\)	\(-48\)	\(132\)	\(18\)

9

New Number: 11.13 | AESZ: | Superseeker: 70/13 15323/39 | Hash: 89df09ff1ec0d5dfcae0791579c9095e

Degree: 11

$13^{2} \theta^4-2 13 x\left(593\theta^4+850\theta^3+685\theta^2+260\theta+39\right)+2^{2} x^{2}\left(81227\theta^4+145178\theta^3+121774\theta^2+52312\theta+9477\right)-x^{3}\left(3180153\theta^4+8754414\theta^3+11733109\theta^2+7260552\theta+1687608\right)+2 x^{4}\left(9121117\theta^4+38823752\theta^3+61935546\theta^2+41745416\theta+10192764\right)-2^{2} x^{5}\left(14736265\theta^4+81359956\theta^3+152008790\theta^2+112521671\theta+29176827\right)+2^{2} 3^{2} x^{6}\left(1220244\theta^4+12211662\theta^3+31283769\theta^2+26817500\theta+7548762\right)+2^{2} 3^{2} x^{7}\left(4505067\theta^4+14797690\theta^3+6324743\theta^2-4986206\theta-2940402\right)-2^{3} 3^{3} x^{8}\left(855097\theta^4+3900198\theta^3+2679311\theta^2-619598\theta-662876\right)-2^{4} 3^{3} x^{9}\left(254021\theta^4+398518\theta^3+352691\theta^2+205022\theta+53940\right)+2^{5} 3^{3} 11 x^{10}\left(13283\theta^4+25990\theta^3+18039\theta^2+5062\theta+456\right)+2^{7} 3^{3} 11^{2} x^{11}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 6, 126, 4092, 160110, ...
--> OEIS
Normalized instanton numbers (n₀=1): 70/13, 420/13, 15323/39, 78225/13, 1564284/13, ... ; Common denominator:...

Discriminant

$(192z^2-69z+1)(2z^3+39z^2-5z+1)(13-112z-18z^2+132z^3)^2$

Local exponents

$0$ ≈$0.064331+0.146063I$ $\infty$ $\frac{ 23}{ 128}+\frac{ 11}{ 384}\sqrt{ 33}$ $\frac{ 23}{ 128}-\frac{ 11}{ 384}\sqrt{ 33}$ ≈$-19.628663$ ≈$0.064331-0.146063I$ ≈$-0.912176$ ≈$0.932793$ ≈$0.115746$
$0$ $0$ $\frac{ 3}{ 4}$ $0$ $0$ $0$ $0$ $0$ $0$ $0$
$0$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$
$0$ $1$ $1$ $1$ $1$ $1$ $1$ $3$ $3$ $3$
$0$ $2$ $\frac{ 5}{ 4}$ $2$ $2$ $2$ $2$ $4$ $4$ $4$

\(0\)	≈\(0.064331+0.146063I\)	\(\infty\)	\(\frac{ 23}{ 128}+\frac{ 11}{ 384}\sqrt{ 33}\)	\(\frac{ 23}{ 128}-\frac{ 11}{ 384}\sqrt{ 33}\)	≈\(-19.628663\)	≈\(0.064331-0.146063I\)	≈\(-0.912176\)	≈\(0.932793\)	≈\(0.115746\)
\(0\)	\(0\)	\(\frac{ 3}{ 4}\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(3\)	\(3\)	\(3\)
\(0\)	\(2\)	\(\frac{ 5}{ 4}\)	\(2\)	\(2\)	\(2\)	\(2\)	\(4\)	\(4\)	\(4\)

Note:

This is operator "11.13" from ...

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

10

New Number: 11.1 | AESZ: | Superseeker: -4 550/3 | Hash: 9e36d74a520997fe52f0cbbfafae6aaf

Degree: 11

$\theta^4+x\left(6+38\theta+96\theta^2+116\theta^3+91\theta^4\right)+x^{2}\left(1218+5950\theta+11076\theta^2+9388\theta^3+3649\theta^4\right)+x^{3}\left(32814+148542\theta+258070\theta^2+203832\theta^3+63585\theta^4\right)+2 x^{4}\left(244543\theta^4+938432\theta^3+1417427\theta^2+933049\theta+226317\right)+2^{2} x^{5}\left(374407\theta^4+1908784\theta^3+3407293\theta^2+2501538\theta+653454\right)+2^{2} 3 x^{6}\left(130530\theta^4+686256\theta^3+1382165\theta^2+1159645\theta+333030\right)+2^{3} x^{7}\left(276464\theta^4-92912\theta^3-3194335\theta^2-3755703\theta-1224450\right)+2^{4} x^{8}\left(341712\theta^4+1614816\theta^3+1576879\theta^2+219863\theta-145632\right)-2^{5} x^{9}\left(29968\theta^4+412128\theta^3+489227\theta^2+156573\theta-3258\right)+2^{8} 3 x^{10}\left(6368\theta^4+13600\theta^3+11014\theta^2+4187\theta+681\right)-2^{11} 3^{2} x^{11}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, -6, 54, 12, -26010, ...
--> OEIS
Normalized instanton numbers (n₀=1): -4, -11, 550/3, -2965/2, -3316, ... ; Common denominator:...

Discriminant

$-(4z+1)(3z+1)(96z^3-1576z^2-62z-1)(1+11z-6z^2+16z^3)^2$

Local exponents

$0$ ≈$0.230478+0.820976I$ $\infty$ $-\frac{ 1}{ 3}$ ≈$-0.085955$ ≈$-0.019642+0.015722I$ $-\frac{ 1}{ 4}$ ≈$0.230478-0.820976I$ ≈$-0.019642-0.015722I$ ≈$16.455951$
$0$ $0$ $\frac{ 3}{ 4}$ $0$ $0$ $0$ $0$ $0$ $0$ $0$
$0$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$
$0$ $3$ $1$ $1$ $3$ $1$ $1$ $3$ $1$ $1$
$0$ $4$ $\frac{ 5}{ 4}$ $2$ $4$ $2$ $2$ $4$ $2$ $2$

\(0\)	≈\(0.230478+0.820976I\)	\(\infty\)	\(-\frac{ 1}{ 3}\)	≈\(-0.085955\)	≈\(-0.019642+0.015722I\)	\(-\frac{ 1}{ 4}\)	≈\(0.230478-0.820976I\)	≈\(-0.019642-0.015722I\)	≈\(16.455951\)
\(0\)	\(0\)	\(\frac{ 3}{ 4}\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(0\)	\(3\)	\(1\)	\(1\)	\(3\)	\(1\)	\(1\)	\(3\)	\(1\)	\(1\)
\(0\)	\(4\)	\(\frac{ 5}{ 4}\)	\(2\)	\(4\)	\(2\)	\(2\)	\(4\)	\(2\)	\(2\)

Note:

This is operator "11.1" from ...

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

11

New Number: 7.13 | AESZ: | Superseeker: -32 -107936 | Hash: 80eaab6a34199e98f88d8472c115c4df

Degree: 7

$\theta^4+2^{4} x\left(44\theta^4+72\theta^3+64\theta^2+28\theta+5\right)+2^{11} x^{2}\left(60\theta^4+328\theta^3+420\theta^2+228\theta+51\right)-2^{18} x^{3}\left(52\theta^4-328\theta^3-885\theta^2-663\theta-181\right)-2^{25} x^{4}\left(148\theta^4+344\theta^3-403\theta^2-559\theta-199\right)-2^{32} x^{5}\left(24\theta^4+544\theta^3+519\theta^2+147\theta-12\right)+2^{39} x^{6}\left(80\theta^4+32\theta^3-147\theta^2-159\theta-46\right)+2^{47} x^{7}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, -80, 10512, -1703168, 309951760, ...
--> OEIS
Normalized instanton numbers (n₀=1): -32, -2840, -107936, -7514224, -575948640, ... ; Common denominator:...

Discriminant

$(64z+1)(128z+1)(128z-1)^2(256z+1)^3$

Local exponents

$0$ $-\frac{ 1}{ 64}$ $\infty$ $-\frac{ 1}{ 128}$ $\frac{ 1}{ 128}$ $-\frac{ 1}{ 256}$
$0$ $0$ $\frac{ 3}{ 4}$ $0$ $0$ $0$
$0$ $1$ $1$ $1$ $1$ $\frac{ 1}{ 4}$
$0$ $1$ $1$ $1$ $3$ $\frac{ 7}{ 4}$
$0$ $2$ $\frac{ 5}{ 4}$ $2$ $4$ $2$

\(0\)	\(-\frac{ 1}{ 64}\)	\(\infty\)	\(-\frac{ 1}{ 128}\)	\(\frac{ 1}{ 128}\)	\(-\frac{ 1}{ 256}\)
\(0\)	\(0\)	\(\frac{ 3}{ 4}\)	\(0\)	\(0\)	\(0\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 4}\)
\(0\)	\(1\)	\(1\)	\(1\)	\(3\)	\(\frac{ 7}{ 4}\)
\(0\)	\(2\)	\(\frac{ 5}{ 4}\)	\(2\)	\(4\)	\(2\)

Note:

This is operator "7.13" from ...

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

12

New Number: 8.20 | AESZ: 213 | Superseeker: 118/17 672 | Hash: d430b37f4ca641af0b82cbef83547c51

Degree: 8

$17^{2} \theta^4-2 17 x\left(647\theta^4+1240\theta^3+977\theta^2+357\theta+51\right)-2^{2} x^{2}\left(14437\theta^4+89752\theta^3+147734\theta^2+92123\theta+20400\right)+2^{2} 3 x^{3}\left(21538\theta^4+25680\theta^3-41979\theta^2-56151\theta-17442\right)+2^{3} x^{4}\left(51920\theta^4+166384\theta^3-83149\theta^2-217017\theta-79362\right)-2^{4} 3 x^{5}\left(9360\theta^4-26784\theta^3-43813\theta^2-21965\theta-3496\right)-2^{5} 3 x^{6}\left(10160\theta^4-96\theta^3-10535\theta^2-5385\theta-438\right)-2^{8} 3^{2} x^{7}\left(288\theta^4+864\theta^3+1082\theta^2+641\theta+147\right)-2^{11} 3^{2} x^{8}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 6, 162, 6252, 290610, ...
--> OEIS
Normalized instanton numbers (n₀=1): 118/17, 873/17, 672, 447987/34, 5358846/17, ... ; Common denominator:...

Discriminant

$-(4z+1)(32z^3+40z^2+78z-1)(-17+18z+48z^2)^2$

Local exponents

$0$ ≈$0.012736$ $-\frac{ 3}{ 16}+\frac{ 1}{ 48}\sqrt{ 897}$ ≈$-0.631368+1.433512I$ ≈$-0.631368-1.433512I$ $-\frac{ 3}{ 16}-\frac{ 1}{ 48}\sqrt{ 897}$ $-\frac{ 1}{ 4}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $\frac{ 3}{ 4}$
$0$ $1$ $1$ $1$ $1$ $1$ $1$ $1$
$0$ $1$ $3$ $1$ $1$ $3$ $1$ $1$
$0$ $2$ $4$ $2$ $2$ $4$ $2$ $\frac{ 5}{ 4}$

\(0\)	≈\(0.012736\)	\(-\frac{ 3}{ 16}+\frac{ 1}{ 48}\sqrt{ 897}\)	≈\(-0.631368+1.433512I\)	≈\(-0.631368-1.433512I\)	\(-\frac{ 3}{ 16}-\frac{ 1}{ 48}\sqrt{ 897}\)	\(-\frac{ 1}{ 4}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 3}{ 4}\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(3\)	\(1\)	\(1\)	\(3\)	\(1\)	\(1\)
\(0\)	\(2\)	\(4\)	\(2\)	\(2\)	\(4\)	\(2\)	\(\frac{ 5}{ 4}\)

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-90\)	\(76\)	\(34\)	\(12\)

13

New Number: 8.24 | AESZ: 286 | Superseeker: 3 437/3 | Hash: 94afcd38a40c3a3e54fc3c57b4b85459

Degree: 8

$3^{2} \theta^4-3^{2} x\left(38\theta^4+82\theta^3+67\theta^2+26\theta+4\right)-3 x^{2}\left(2045\theta^4+5702\theta^3+7535\theta^2+4170\theta+852\right)+2^{3} 3 x^{3}\left(2208\theta^4+5925\theta^3+7925\theta^2+5607\theta+1512\right)+2^{3} x^{4}\left(60287\theta^4+56374\theta^3-215983\theta^2-268986\theta-85452\right)-2^{4} x^{5}\left(205651\theta^4+605608\theta^3+603579\theta^2+204622\theta+8104\right)-2^{7} x^{6}\left(51414\theta^4-273267\theta^3-502700\theta^2-305649\theta-63398\right)+2^{8} 37 x^{7}\left(7909\theta^4+18122\theta^3+17595\theta^2+8462\theta+1672\right)-2^{13} 37^{2} x^{8}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 4, 72, 1696, 49960, ...
--> OEIS
Normalized instanton numbers (n₀=1): 3, 539/24, 437/3, 18531/8, 90274/3, ... ; Common denominator:...

Discriminant

$-(-1+40z+504z^2-3088z^3+8192z^4)(-3-3z+148z^2)^2$

Local exponents

$0$ ≈$0.213707$ ≈$-0.070843$ ≈$0.213707$ $\frac{ 3}{ 296}-\frac{ 1}{ 296}\sqrt{ 1785}$ $\infty$ $\frac{ 3}{ 296}+\frac{ 1}{ 296}\sqrt{ 1785}$ ≈$0.020383$
$0$ $0$ $0$ $0$ $0$ $\frac{ 3}{ 4}$ $0$ $0$
$0$ $1$ $1$ $1$ $1$ $1$ $1$ $1$
$0$ $1$ $1$ $1$ $3$ $1$ $3$ $1$
$0$ $2$ $2$ $2$ $4$ $\frac{ 5}{ 4}$ $4$ $2$

\(0\)	≈\(0.213707\)	≈\(-0.070843\)	≈\(0.213707\)	\(\frac{ 3}{ 296}-\frac{ 1}{ 296}\sqrt{ 1785}\)	\(\infty\)	\(\frac{ 3}{ 296}+\frac{ 1}{ 296}\sqrt{ 1785}\)	≈\(0.020383\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 3}{ 4}\)	\(0\)	\(0\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)	\(3\)	\(1\)	\(3\)	\(1\)
\(0\)	\(2\)	\(2\)	\(2\)	\(4\)	\(\frac{ 5}{ 4}\)	\(4\)	\(2\)

Note:

This is operator "8.24" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-86\)	\(84\)	\(48\)	\(15\)

14

New Number: 8.39 | AESZ: | Superseeker: -12/5 136/3 | Hash: c1330764e09752f7bb8e86b15541c588

Degree: 8

$5^{2} \theta^4+2 3 5 x\left(51\theta^4+84\theta^3+72\theta^2+30\theta+5\right)+2^{2} 3 x^{2}\left(3297\theta^4+10236\theta^3+13562\theta^2+8110\theta+1830\right)+2^{2} 3^{3} x^{3}\left(3866\theta^4+14088\theta^3+21137\theta^2+14355\theta+3600\right)+2^{3} 3^{3} x^{4}\left(11680\theta^4+38792\theta^3+45641\theta^2+24205\theta+4854\right)+2^{4} 3^{5} x^{5}\left(2624\theta^4+8240\theta^3+8275\theta^2+2971\theta+216\right)+2^{5} 3^{5} x^{6}\left(3248\theta^4+8832\theta^3+9739\theta^2+4803\theta+882\right)+2^{7} 3^{7} x^{7}\left(144\theta^4+384\theta^3+428\theta^2+233\theta+51\right)+2^{9} 3^{7} x^{8}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, -6, 54, -348, -3690, ...
--> OEIS
Normalized instanton numbers (n₀=1): -12/5, -21/5, 136/3, -1743/10, -1056/5, ... ; Common denominator:...

Discriminant

$(1+54z+1152z^2+6048z^3+3456z^4)(5+18z+72z^2)^2$

Local exponents

$0$ $\infty$ ≈$-0.152177$ ≈$-1.540068$ $-\frac{ 1}{ 8}+\frac{ 1}{ 24}\sqrt{ 31}I$ ≈$-0.028878$ ≈$-0.028878$ $-\frac{ 1}{ 8}-\frac{ 1}{ 24}\sqrt{ 31}I$
$0$ $\frac{ 3}{ 4}$ $0$ $0$ $0$ $0$ $0$ $0$
$0$ $1$ $1$ $1$ $1$ $1$ $1$ $1$
$0$ $1$ $1$ $1$ $3$ $1$ $1$ $3$
$0$ $\frac{ 5}{ 4}$ $2$ $2$ $4$ $2$ $2$ $4$

\(0\)	\(\infty\)	≈\(-0.152177\)	≈\(-1.540068\)	\(-\frac{ 1}{ 8}+\frac{ 1}{ 24}\sqrt{ 31}I\)	≈\(-0.028878\)	≈\(-0.028878\)	\(-\frac{ 1}{ 8}-\frac{ 1}{ 24}\sqrt{ 31}I\)
\(0\)	\(\frac{ 3}{ 4}\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)	\(3\)	\(1\)	\(1\)	\(3\)
\(0\)	\(\frac{ 5}{ 4}\)	\(2\)	\(2\)	\(4\)	\(2\)	\(2\)	\(4\)

Note:

This is operator "8.39" from ...

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

15

New Number: 8.75 | AESZ: | Superseeker: -100/3 66364 | Hash: 76a0af78cc3434c7a78f3edc406baa61

Degree: 8

$3^{2} \theta^4+2^{2} 3 x\left(592\theta^4+992\theta^3+913\theta^2+417\theta+78\right)+2^{7} x^{2}\left(17984\theta^4+49280\theta^3+67508\theta^2+43356\theta+10623\right)+2^{15} x^{3}\left(13472\theta^4+38976\theta^3+56498\theta^2+42534\theta+11589\right)+2^{21} x^{4}\left(29248\theta^4+79232\theta^3+81724\theta^2+43620\theta+8603\right)+2^{30} x^{5}\left(5760\theta^4+15936\theta^3+16712\theta^2+5206\theta-123\right)+2^{37} x^{6}\left(3200\theta^4+8064\theta^3+10616\theta^2+6036\theta+1263\right)+2^{47} x^{7}\left(160\theta^4+416\theta^3+466\theta^2+255\theta+56\right)+2^{55} x^{8}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, -104, 16488, -3037568, 605558440, ...
--> OEIS
Normalized instanton numbers (n₀=1): -100/3, 538/3, 66364, 9836374/3, 67135456/3, ... ; Common denominator:...

Discriminant

$(64z+1)(128z+1)(256z+1)^2(32768z^2+128z+3)^2$

Local exponents

$0$ $-\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 23}I$ $\infty$ $-\frac{ 1}{ 128}$ $-\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 23}I$ $-\frac{ 1}{ 64}$ $-\frac{ 1}{ 256}$
$0$ $0$ $\frac{ 3}{ 4}$ $0$ $0$ $0$ $0$
$0$ $1$ $1$ $1$ $1$ $1$ $0$
$0$ $3$ $1$ $1$ $3$ $1$ $1$
$0$ $4$ $\frac{ 5}{ 4}$ $2$ $4$ $2$ $1$

\(0\)	\(-\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 23}I\)	\(\infty\)	\(-\frac{ 1}{ 128}\)	\(-\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 23}I\)	\(-\frac{ 1}{ 64}\)	\(-\frac{ 1}{ 256}\)
\(0\)	\(0\)	\(\frac{ 3}{ 4}\)	\(0\)	\(0\)	\(0\)	\(0\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(0\)
\(0\)	\(3\)	\(1\)	\(1\)	\(3\)	\(1\)	\(1\)
\(0\)	\(4\)	\(\frac{ 5}{ 4}\)	\(2\)	\(4\)	\(2\)	\(1\)

Note:

This is operator "8.75" from ...

\(cy[DM_basis]\)	\(\)	\(\)	\(\)
\(\)	\(\)	\(\)	\(\)
\(\)	\(\)	\(\)	\(\)
\(\)	\(\)	\(\)	\(\)

\(16.+8.373926794I\)	\(-5-576\lambda\)	\(\frac{ 5}{ 4}+144\lambda\)	\(-.204864220-.332298682I\)
\(63\)	\(-20\)	\(\frac{ 21}{ 4}\)	\(-\frac{ 5}{ 4}-144\lambda\)
\(252\)	\(-84\)	\(22\)	\(-5-576\lambda\)
\(756+\frac{ 1}{ 500000000}I\)	\(-252\)	\(63\)	\(-14.-8.373926794I\)

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

\(\frac{ 11}{ 12}\)	\(-152\lambda\)	\(\frac{ 23}{ 288}\)	\(0\)
\(0\)	\(-\frac{ 11}{ 12}\)	\(0\)	\(\frac{ 23}{ 288}\)
\(2\)	\(0\)	\(-\frac{ 11}{ 12}\)	\(152\lambda\)
\(0\)	\(2\)	\(0\)	\(\frac{ 11}{ 12}\)

\(1+96\lambda\)	\(0\)	\(8\lambda\)	\(.5153046e-2\)
\(\frac{ 7}{ 2}\)	\(1\)	\(\frac{ 7}{ 24}\)	\(-8\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(42\)	\(0\)	\(\frac{ 7}{ 2}\)	\(1-96\lambda\)

\(-96\lambda\)	\(\frac{ 21}{ 2}\)	\(1\)	\(1\)
\(-\frac{ 7}{ 2}\)	\(-21\)	\(-1\)	\(0\)
\(0\)	\(42\)	\(0\)	\(0\)
\(-42\)	\(0\)	\(0\)	\(0\)

\(1+96\lambda\)	\(\frac{ 1}{ 4}\)	\(-4\lambda\)	\(.5907751e-2\)
\(2\)	\(1\)	\(-\frac{ 1}{ 12}\)	\(4\lambda\)
\(0\)	\(6\)	\(1\)	\(\frac{ 1}{ 4}\)
\(-48\)	\(0\)	\(2\)	\(1-96\lambda\)

\(-96\lambda\)	\(-6\)	\(1\)	\(1\)
\(-2\)	\(24\)	\(-1\)	\(0\)
\(0\)	\(-48\)	\(0\)	\(0\)
\(48\)	\(0\)	\(0\)	\(0\)

Calabi-Yau differential operator database v.3

Summary

Discriminant

Local exponents

Note:

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:

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

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:

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

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:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant