Calabi-Yau differential operator database v.3.0

1

New Number: 2.54 | AESZ: 41 | Superseeker: 2 -104 | Hash: a9ddeed4299f59fb9ac9f6f248383b8f

Degree: 2

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

Coefficients of the holomorphic solution: 1, 6, 54, 60, -19530, ...
--> OEIS
Normalized instanton numbers (n₀=1): 2, -7, -104, -588, 3300, ... ; Common denominator:...

Discriminant

$1-56z+1296z^2$

Local exponents

$0$ $\frac{ 7}{ 324}-\frac{ 1}{ 81}\sqrt{ 2}I$ $\frac{ 7}{ 324}+\frac{ 1}{ 81}\sqrt{ 2}I$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $1$
$0$ $1$ $1$ $1$
$0$ $2$ $2$ $\frac{ 3}{ 2}$

\(0\)	\(\frac{ 7}{ 324}-\frac{ 1}{ 81}\sqrt{ 2}I\)	\(\frac{ 7}{ 324}+\frac{ 1}{ 81}\sqrt{ 2}I\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)
\(0\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

Hadamard product $I \ast \delta$

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

2

New Number: 3.24 | AESZ: | Superseeker: -2 -108 | Hash: 3c89cc2017daa2eba88c016b8ae5865c

Degree: 3

$\theta^4+2 x(2\theta+1)^2(3\theta^2+3\theta+1)-2^{2} x^{2}(2\theta+1)(2\theta+3)(47\theta^2+94\theta+51)+2^{4} 7 x^{3}(2\theta+1)(2\theta+3)^2(2\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, -2, 54, -980, 26950, ...
--> OEIS
Normalized instanton numbers (n₀=1): -2, 17, -108, 1498, -19630, ... ; Common denominator:...

Discriminant

$(16z-1)(112z^2-40z-1)$

Local exponents

$\frac{ 5}{ 28}-\frac{ 1}{ 7}\sqrt{ 2}$ $0$ $\frac{ 1}{ 16}$ $\frac{ 5}{ 28}+\frac{ 1}{ 7}\sqrt{ 2}$ $\infty$
$0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $1$ $\frac{ 3}{ 2}$
$1$ $0$ $1$ $1$ $\frac{ 3}{ 2}$
$2$ $0$ $2$ $2$ $\frac{ 5}{ 2}$

\(\frac{ 5}{ 28}-\frac{ 1}{ 7}\sqrt{ 2}\)	\(0\)	\(\frac{ 1}{ 16}\)	\(\frac{ 5}{ 28}+\frac{ 1}{ 7}\sqrt{ 2}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(0\)	\(1\)	\(1\)	\(\frac{ 3}{ 2}\)
\(1\)	\(0\)	\(1\)	\(1\)	\(\frac{ 3}{ 2}\)
\(2\)	\(0\)	\(2\)	\(2\)	\(\frac{ 5}{ 2}\)

Note:

This is operator $\tilde{C_9}$

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-296\)	\(160\)	\(112\)	\(32\)

3

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

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

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

Note:

This is operator "5.102" from ...

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

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

4

New Number: 5.124 | AESZ: | Superseeker: 307 4336475 | Hash: 782c2ecb639a2462baac59dfaf17de0e

Degree: 5

$\theta^4-x\left(1081\theta^4+2594\theta^3+1807\theta^2+510\theta+54\right)-2^{2} 3^{2} x^{2}\left(4686\theta^4+4908\theta^3-2213\theta^2-1738\theta-293\right)-2^{2} 3^{4} x^{3}\left(18484\theta^4-3336\theta^3-4883\theta^2-1101\theta-50\right)+2^{5} 3^{7} x^{4}(2\theta+1)(92\theta^3+134\theta^2+79\theta+17)-2^{8} 3^{8} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 54, 19746, 11427300, 8114331330, ...
--> OEIS
Normalized instanton numbers (n₀=1): 307, 19410, 4336475, 1291393654, 484327566649, ... ; Common denominator:...

Discriminant

$-(z-1)(1296z^2-1224z+1)(1+72z)^2$

Local exponents

$-\frac{ 1}{ 72}$ $0$ $\frac{ 17}{ 36}-\frac{ 1}{ 3}\sqrt{ 2}$ $\frac{ 17}{ 36}+\frac{ 1}{ 3}\sqrt{ 2}$ $1$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $1$ $1$ $1$
$3$ $0$ $1$ $1$ $1$ $1$
$4$ $0$ $2$ $2$ $2$ $\frac{ 3}{ 2}$

\(-\frac{ 1}{ 72}\)	\(0\)	\(\frac{ 17}{ 36}-\frac{ 1}{ 3}\sqrt{ 2}\)	\(\frac{ 17}{ 36}+\frac{ 1}{ 3}\sqrt{ 2}\)	\(1\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(1\)
\(3\)	\(0\)	\(1\)	\(1\)	\(1\)	\(1\)
\(4\)	\(0\)	\(2\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

B-Incarnation as fibre product 62211- x 263--1

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

5

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

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

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

Note:

This is operator "5.49" from ...

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

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

6

New Number: 5.94 | AESZ: 334 | Superseeker: 7/3 -4843/81 | Hash: 1ab1dce2847b14dd89a8f8f48ddc7214

Degree: 5

$3^{2} \theta^4-3 x\left(166\theta^4+320\theta^3+271\theta^2+111\theta+18\right)+x^{2}\left(11155\theta^4+42652\theta^3+60463\theta^2+36876\theta+8172\right)-3^{2} x^{3}\left(4705\theta^4+23418\theta^3+42217\theta^2+31152\theta+7932\right)+2^{2} 3 x^{4}\left(3514\theta^4+16403\theta^3+25581\theta^2+16442\theta+3744\right)-2^{2} 5 x^{5}(5\theta+3)(5\theta+4)(5\theta+6)(5\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 6, 54, 240, -9450, ...
--> OEIS
Normalized instanton numbers (n₀=1): 7/3, -79/12, -4843/81, -1058/3, 3620/3, ... ; Common denominator:...

Discriminant

$-(3125z^3-1167z^2+54z-1)(2z-3)^2$

Local exponents

$0$ ≈$0.025215-0.018839I$ ≈$0.025215+0.018839I$ ≈$0.32301$ $\frac{ 3}{ 2}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 3}{ 5}$
$0$ $1$ $1$ $1$ $1$ $\frac{ 4}{ 5}$
$0$ $1$ $1$ $1$ $3$ $\frac{ 6}{ 5}$
$0$ $2$ $2$ $2$ $4$ $\frac{ 7}{ 5}$

\(0\)	≈\(0.025215-0.018839I\)	≈\(0.025215+0.018839I\)	≈\(0.32301\)	\(\frac{ 3}{ 2}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 3}{ 5}\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(\frac{ 4}{ 5}\)
\(0\)	\(1\)	\(1\)	\(1\)	\(3\)	\(\frac{ 6}{ 5}\)
\(0\)	\(2\)	\(2\)	\(2\)	\(4\)	\(\frac{ 7}{ 5}\)

Note:

This is operator "5.94" from ...

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

7

New Number: 5.99 | AESZ: 342 | Superseeker: -4 3856/9 | Hash: 009a00efdd065ef9ea58db999d777786

Degree: 5

$\theta^4+2 x\left(50\theta^4+64\theta^3+52\theta^2+20\theta+3\right)+2^{2} 3 x^{2}\left(380\theta^4+992\theta^3+1166\theta^2+612\theta+117\right)+2^{2} 3^{2} x^{3}\left(2140\theta^4+5832\theta^3+5651\theta^2+2349\theta+360\right)+2^{4} 3^{6} x^{4}(2\theta+1)(20\theta^3+42\theta^2+35\theta+11)+2^{6} 3^{7} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, -6, 54, 660, -69930, ...
--> OEIS
Normalized instanton numbers (n₀=1): -4, -16, 3856/9, -3864, -20784, ... ; Common denominator:...

Discriminant

$(3888z^3+2592z^2+76z+1)(1+12z)^2$

Local exponents

≈$-0.636595$ $-\frac{ 1}{ 12}$ ≈$-0.015036-0.01334I$ ≈$-0.015036+0.01334I$ $0$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $1$ $1$ $0$ $1$
$1$ $3$ $1$ $1$ $0$ $1$
$2$ $4$ $2$ $2$ $0$ $\frac{ 3}{ 2}$

≈\(-0.636595\)	\(-\frac{ 1}{ 12}\)	≈\(-0.015036-0.01334I\)	≈\(-0.015036+0.01334I\)	\(0\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(1\)	\(1\)	\(0\)	\(1\)
\(1\)	\(3\)	\(1\)	\(1\)	\(0\)	\(1\)
\(2\)	\(4\)	\(2\)	\(2\)	\(0\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.99" from ...

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

8

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

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

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

Note:

This is operator "11.1" from ...

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

9

New Number: 12.7 | AESZ: | Superseeker: -24/7 117 | Hash: fedf397077a0af56af404f5156e1b5c0

Degree: 12

$7^{2} \theta^4+2 3 7 x\left(111\theta^4+120\theta^3+102\theta^2+42\theta+7\right)+2^{2} 3 x^{2}\left(16827\theta^4+34008\theta^3+38464\theta^2+20846\theta+4494\right)+3^{3} x^{3}\left(178553\theta^4+439878\theta^3+528099\theta^2+313502\theta+74536\right)+2 3^{3} x^{4}\left(1355053\theta^4+3438698\theta^3+3854711\theta^2+2221354\theta+519896\right)+2^{2} 3^{4} x^{5}\left(2406561\theta^4+5708802\theta^3+5082043\theta^2+2161754\theta+336752\right)+2^{3} 3^{5} x^{6}\left(3133411\theta^4+6625998\theta^3+4266961\theta^2+238710\theta-485736\right)+2^{6} 3^{6} x^{7}\left(746186\theta^4+1366021\theta^3+743388\theta^2-203279\theta-212552\right)+2^{7} 3^{7} x^{8}\left(506499\theta^4+760668\theta^3+404459\theta^2-112958\theta-117216\right)+2^{11} 3^{8} x^{9}\left(27992\theta^4+34962\theta^3+7197\theta^2-14685\theta-7604\right)+2^{14} 3^{9} x^{10}\left(1381\theta^4+1244\theta^3-2460\theta^2-4030\theta-1571\right)-2^{18} 3^{10} x^{11}(22\theta^2+98\theta+105)(\theta+1)^2-2^{22} 3^{11} x^{12}(\theta+1)^2(\theta+2)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, -6, 54, -276, -8442, ...
--> OEIS
Normalized instanton numbers (n₀=1): -24/7, -24/7, 117, -564, 948/7, ... ; Common denominator:...

Discriminant

$-(6z+1)(10368z^5-864z^4-7371z^3-1440z^2-60z-1)(7+102z+648z^2+3456z^3)^2$

Local exponents

$-\frac{ 1}{ 6}$ ≈$-0.097659$ ≈$-0.04492-0.136829I$ ≈$-0.04492+0.136829I$ $0$ $#ND+#NDI$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $1$
$1$ $1$ $1$ $1$ $0$ $1$ $1$
$1$ $3$ $3$ $3$ $0$ $1$ $2$
$2$ $4$ $4$ $4$ $0$ $2$ $2$

\(-\frac{ 1}{ 6}\)	≈\(-0.097659\)	≈\(-0.04492-0.136829I\)	≈\(-0.04492+0.136829I\)	\(0\)	\(#ND+#NDI\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(1\)	\(1\)	\(1\)	\(0\)	\(1\)	\(1\)
\(1\)	\(3\)	\(3\)	\(3\)	\(0\)	\(1\)	\(2\)
\(2\)	\(4\)	\(4\)	\(4\)	\(0\)	\(2\)	\(2\)

Note:

This is operator "12.7" from ...

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

10

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

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

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

Note:

This is operator "8.39" from ...

\(.872284041I\)	\(-\frac{ 1}{ 6}+30\lambda\)	\(-\frac{ 1}{ 12}+15\lambda\)	\(-\frac{ 1}{ 243}\sqrt{ 3}ln(2)^2/(-8I\lambdaPi^3)^(\frac{ 1}{ 6})+5\lambda\)
\(6\)	\(2\)	\(\frac{ 1}{ 2}\)	\(\frac{ 1}{ 12}-15\lambda\)
\(-12\)	\(-2\)	\(0\)	\(-\frac{ 1}{ 6}+30\lambda\)
\(72\)	\(12\)	\(6\)	\(2.-.872284041I\)

\(2.+.872284041I\)	\(-\frac{ 1}{ 6}-30\lambda\)	\(\frac{ 1}{ 12}+15\lambda\)	\(-\frac{ 1}{ 243}\sqrt{ 3}ln(2)^2/(-8I\lambdaPi^3)^(\frac{ 1}{ 6})-5\lambda\)
\(6\)	\(0\)	\(\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 12}-15\lambda\)
\(12\)	\(-2\)	\(2\)	\(-\frac{ 1}{ 6}-30\lambda\)
\(72\)	\(-12\)	\(6\)	\(-.872284041I\)

\(1-\frac{ 872284041}{ 1000000000}I\)	\(24\)	\(\frac{ 7}{ 6}\)	\(1\)
\(-6\)	\(-48\)	\(-1\)	\(0\)
\(12\)	\(72\)	\(0\)	\(0\)
\(-72\)	\(0\)	\(0\)	\(0\)

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:

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:

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