Calabi-Yau differential operator database v.3.0

1

New Number: 2.24 | AESZ: 137 | Superseeker: 20 1684/3 | Hash: 198d6c822d6c46225ac2553d60df6539

Degree: 2

$\theta^4-2^{2} x(2\theta+1)^2(17\theta^2+17\theta+6)+2^{7} 3^{2} x^{2}(2\theta+1)^2(2\theta+3)^2$

Coefficients of the holomorphic solution: 1, 24, 1512, 124800, 11730600, ...
--> OEIS
Normalized instanton numbers (n₀=1): 20, 2, 1684/3, 7602, 173472, ... ; Common denominator:...

Discriminant

$(144z-1)(128z-1)$

Local exponents

$0$ $\frac{ 1}{ 144}$ $\frac{ 1}{ 128}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $\frac{ 3}{ 2}$
$0$ $2$ $2$ $\frac{ 3}{ 2}$

\(0\)	\(\frac{ 1}{ 144}\)	\(\frac{ 1}{ 128}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 3}{ 2}\)
\(0\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

Hadamard product $A \ast g$.

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-16\)	\(96\)	\(48\)	\(16\)

2

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

Degree: 2

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

Maple LaTex

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 $I \ast \delta$

3

New Number: 2.57 | AESZ: 184 | Superseeker: 2 -8 | Hash: ee8bb517b329e58eeb4352dc3cdc3f81

Degree: 2

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 10, 210, 5500, 159250, ...
--> OEIS
Normalized instanton numbers (n₀=1): 2, 4, -8, -194, -2820, ... ; Common denominator:...

Discriminant

$1-88z+2000z^2$

Local exponents

$0$ $\frac{ 11}{ 500}-\frac{ 1}{ 250}I$ $\frac{ 11}{ 500}+\frac{ 1}{ 250}I$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $1$
$0$ $1$ $1$ $1$
$0$ $2$ $2$ $\frac{ 3}{ 2}$

\(0\)	\(\frac{ 11}{ 500}-\frac{ 1}{ 250}I\)	\(\frac{ 11}{ 500}+\frac{ 1}{ 250}I\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)
\(0\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

Hadamard product $I \ast \eta$

Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 2, 34, -214, -12382, -352498, -6554486, -92778754,...
Coefficients of the q-coordinate : 0, 1, -22, 359, -4892, 61955, -725338, 8256993,...

	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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$.16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667+.969204490I$	$-\frac{ 1}{ 12}+20\lambda$	$-\frac{ 1}{ 18}+\frac{ 40}{ 3}\lambda$	$.2449129e-2+\frac{ 10}{ 3}\lambda$
$\frac{ 20}{ 3}$	$\frac{ 5}{ 3}$	$\frac{ 4}{ 9}$	$\frac{ 1}{ 18}-\frac{ 40}{ 3}\lambda$
$-10$	$-1$	$\frac{ 1}{ 3}$	$-\frac{ 1}{ 12}+20\lambda$
$100$	$10$	$\frac{ 20}{ 3}$	$1.8333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-.969204490I$

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$1.8333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333+.969204490I$	$-\frac{ 1}{ 12}-20\lambda$	$\frac{ 1}{ 18}+\frac{ 40}{ 3}\lambda$	$.2449129e-2-\frac{ 10}{ 3}\lambda$
$\frac{ 20}{ 3}$	$\frac{ 1}{ 3}$	$\frac{ 4}{ 9}$	$-\frac{ 1}{ 18}-\frac{ 40}{ 3}\lambda$
$10$	$-1$	$\frac{ 5}{ 3}$	$-\frac{ 1}{ 12}-20\lambda$
$100$	$-10$	$\frac{ 20}{ 3}$	$.16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667-.969204490I$

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Basis of the Doran-Morgan lattice

$\frac{ 5}{ 6}-\frac{ 96920449}{ 100000000}I$	$\frac{ 85}{ 3}$	$\frac{ 11}{ 10}$	$1$
$-\frac{ 20}{ 3}$	$-60$	$-1$	$0$
$10$	$100$	$0$	$0$
$-100$	$0$	$0$	$0$

copy data

4

New Number: 3.1 | AESZ: 34 | Superseeker: 1 28/3 | Hash: e5461c5f5ae4d929328f66b8955a31f5

Degree: 3

$\theta^4-x\left(35\theta^4+70\theta^3+63\theta^2+28\theta+5\right)+x^{2}(\theta+1)^2(259\theta^2+518\theta+285)-3^{2} 5^{2} x^{3}(\theta+1)^2(\theta+2)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 5, 45, 545, 7885, ...
--> OEIS
Normalized instanton numbers (n₀=1): 1, 2, 28/3, 52, 350, ... ; Common denominator:...

Discriminant

$-(z-1)(25z-1)(9z-1)$

Local exponents

$0$ $\frac{ 1}{ 25}$ $\frac{ 1}{ 9}$ $1$ $\infty$
$0$ $0$ $0$ $0$ $1$
$0$ $1$ $1$ $1$ $1$
$0$ $1$ $1$ $1$ $2$
$0$ $2$ $2$ $2$ $2$

\(0\)	\(\frac{ 1}{ 25}\)	\(\frac{ 1}{ 9}\)	\(1\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)	\(2\)
\(0\)	\(2\)	\(2\)	\(2\)	\(2\)

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-80\)	\(120\)	\(120\)	\(30\)

5

New Number: 3.26 | AESZ: 407 | Superseeker: 2 440 | Hash: c46d32ba4b3738ba34fe1e6c16e6f242

Degree: 3

$\theta^4+2 x\left(132\theta^4+264\theta^3+293\theta^2+161\theta+35\right)+2^{2} 5^{2} x^{2}(\theta+1)^2(228\theta^2+456\theta+335)+2^{6} 5^{4} x^{3}(\theta+1)(\theta+2)(4\theta+5)(4\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, -70, 5650, -484900, 43071250, ...
--> OEIS
Normalized instanton numbers (n₀=1): 2, -44, 440, -4844, 46268, ... ; Common denominator:...

Discriminant

$(64z+1)(1+100z)^2$

Local exponents

$-\frac{ 1}{ 64}$ $-\frac{ 1}{ 100}$ $0$ $\infty$
$0$ $0$ $0$ $1$
$1$ $-\frac{ 1}{ 2}$ $0$ $\frac{ 5}{ 4}$
$1$ $1$ $0$ $\frac{ 7}{ 4}$
$2$ $\frac{ 3}{ 2}$ $0$ $2$

\(-\frac{ 1}{ 64}\)	\(-\frac{ 1}{ 100}\)	\(0\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(-\frac{ 1}{ 2}\)	\(0\)	\(\frac{ 5}{ 4}\)
\(1\)	\(1\)	\(0\)	\(\frac{ 7}{ 4}\)
\(2\)	\(\frac{ 3}{ 2}\)	\(0\)	\(2\)

Note:

This is operator "3.26" from ...

6

New Number: 10.3 | AESZ: | Superseeker: 2 421/9 | Hash: 5219414e025733d8e128028821370b4b

Degree: 10

$\theta^4-x\left(321\theta^4+258\theta^3+258\theta^2+129\theta+26\right)+x^{2}\left(74028\theta^3+14112+55150\theta+89219\theta^2+46467\theta^4\right)-2^{3} x^{3}\left(499260\theta^4+1184748\theta^3+1665809\theta^2+1187841\theta+345452\right)+2^{4} 3 x^{4}\left(4702665\theta^4+14805730\theta^3+23754818\theta^2+18867201\theta+5979118\right)-2^{6} x^{5}\left(136927125\theta^4+537349854\theta^3+968406086\theta^2+839579917\theta+283906432\right)+2^{6} x^{6}\left(3697617171\theta^4+17401686816\theta^3+34821823585\theta^2+32540314464\theta+11600569724\right)-2^{9} x^{7}\left(8571324186\theta^4+47135706036\theta^3+103830096399\theta^2+103713883221\theta+38684901782\right)+2^{12} x^{8}\left(13055773347\theta^4+82367586444\theta^3+198438600506\theta^2+210671505052\theta+81797663483\right)-2^{16} 137 x^{9}(2\theta+3)(21527774\theta^3+121431015\theta^2+220937755\theta+121634574)+2^{20} 3 73^{2} 137^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 26, 730, 21320, 638506, ...
--> OEIS
Normalized instanton numbers (n₀=1): 2, -3/2, 421/9, -519/2, 285, ... ; Common denominator:...

Discriminant

$(24z-1)(42632z^3-3675z^2+105z-1)(32z-1)^2(1096z^2-64z+1)^2$

Local exponents

$0$ ≈$0.025716-0.003646I$ ≈$0.025716+0.003646I$ $\frac{ 4}{ 137}-\frac{ 3}{ 548}\sqrt{ 2}I$ $\frac{ 4}{ 137}+\frac{ 3}{ 548}\sqrt{ 2}I$ $\frac{ 1}{ 32}$ ≈$0.034771$ $\frac{ 1}{ 24}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $1$
$0$ $1$ $1$ $1$ $1$ $\frac{ 1}{ 2}$ $1$ $1$ $\frac{ 3}{ 2}$
$0$ $1$ $1$ $3$ $3$ $\frac{ 1}{ 2}$ $1$ $1$ $\frac{ 5}{ 2}$
$0$ $2$ $2$ $4$ $4$ $1$ $2$ $2$ $3$

\(0\)	≈\(0.025716-0.003646I\)	≈\(0.025716+0.003646I\)	\(\frac{ 4}{ 137}-\frac{ 3}{ 548}\sqrt{ 2}I\)	\(\frac{ 4}{ 137}+\frac{ 3}{ 548}\sqrt{ 2}I\)	\(\frac{ 1}{ 32}\)	≈\(0.034771\)	\(\frac{ 1}{ 24}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)	\(1\)	\(1\)	\(\frac{ 3}{ 2}\)
\(0\)	\(1\)	\(1\)	\(3\)	\(3\)	\(\frac{ 1}{ 2}\)	\(1\)	\(1\)	\(\frac{ 5}{ 2}\)
\(0\)	\(2\)	\(2\)	\(4\)	\(4\)	\(1\)	\(2\)	\(2\)	\(3\)

Note:

This is operator "10.3" from ...

7

New Number: 13.6 | AESZ: | Superseeker: 2 421/9 | Hash: 679aa37a05aafe03e8d68785d566fcfb

Degree: 13

\(\theta^4-x\left(217\theta^4+178\theta^3+178\theta^2+89\theta+18\right)+x^{2}\left(6192+24334\theta+39795\theta^2+33324\theta^3+20643\theta^4\right)-2^{3} x^{3}\left(139307\theta^4+333558\theta^3+457560\theta^2+315505\theta+89244\right)+2^{4} x^{4}\left(2283535\theta^4+7259062\theta^3+11103058\theta^2+8192571\theta+2419362\right)-2^{6} 3 x^{5}\left(3630237\theta^4+14551206\theta^3+23954402\theta^2+17624013\theta+4953960\right)+2^{6} 3^{2} x^{6}\left(9379387\theta^4+48172928\theta^3+74157721\theta^2+31932048\theta-1833876\right)+2^{9} 3^{5} x^{7}\left(495945\theta^4+2307886\theta^3+6892788\theta^2+10676039\theta+5452406\right)-2^{12} 3^{4} x^{8}\left(5269994\theta^4+31826568\theta^3+83327461\theta^2+106595346\theta+49104855\right)+2^{15} 3^{7} x^{9}\left(129774\theta^4+976140\theta^3+2673571\theta^2+3442327\theta+1597000\right)+2^{18} 3^{10} x^{10}(\theta+1)(6759\theta^3+40481\theta^2+97855\theta+79397)-2^{21} 3^{9} x^{11}(\theta+1)(\theta+2)(29107\theta^2+160713\theta+251822)-2^{27} 3^{12} x^{12}(\theta+3)(\theta+2)(\theta+1)(17\theta+4)+2^{29} 3^{15} 5 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple LaTex

Coefficients of the holomorphic solution: 1, 18, 378, 8280, 187434, ...
--> OEIS
Normalized instanton numbers (n₀=1): 2, -3/2, 421/9, -519/2, 285, ... ; Common denominator:...

Discriminant

$(16z-1)(19440z^3-2187z^2+81z-1)(24z-1)^2(648z^2-48z+1)^2(8z+1)^3$

Local exponents

$-\frac{ 1}{ 8}$ $0$ ≈$0.032165-0.005771I$ ≈$0.032165+0.005771I$ $\frac{ 1}{ 27}-\frac{ 1}{ 108}\sqrt{ 2}I$ $\frac{ 1}{ 27}+\frac{ 1}{ 108}\sqrt{ 2}I$ $\frac{ 1}{ 24}$ ≈$0.04817$ $\frac{ 1}{ 16}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $1$
$\frac{ 1}{ 2}$ $0$ $1$ $1$ $1$ $1$ $\frac{ 1}{ 2}$ $1$ $1$ $2$
$\frac{ 3}{ 2}$ $0$ $1$ $1$ $3$ $3$ $\frac{ 1}{ 2}$ $1$ $1$ $3$
$2$ $0$ $2$ $2$ $4$ $4$ $1$ $2$ $2$ $4$

\(-\frac{ 1}{ 8}\)	\(0\)	≈\(0.032165-0.005771I\)	≈\(0.032165+0.005771I\)	\(\frac{ 1}{ 27}-\frac{ 1}{ 108}\sqrt{ 2}I\)	\(\frac{ 1}{ 27}+\frac{ 1}{ 108}\sqrt{ 2}I\)	\(\frac{ 1}{ 24}\)	≈\(0.04817\)	\(\frac{ 1}{ 16}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(\frac{ 1}{ 2}\)	\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)	\(1\)	\(1\)	\(2\)
\(\frac{ 3}{ 2}\)	\(0\)	\(1\)	\(1\)	\(3\)	\(3\)	\(\frac{ 1}{ 2}\)	\(1\)	\(1\)	\(3\)
\(2\)	\(0\)	\(2\)	\(2\)	\(4\)	\(4\)	\(1\)	\(2\)	\(2\)	\(4\)

Note:

This is operator "13.6" from ...

8

New Number: 14.10 | AESZ: | Superseeker: 2 38 | Hash: 364dddcd3359111a8e01be8efc1de60c

Degree: 14

\(\theta^4+2 x\left(72\theta^4+48\theta^3+59\theta^2+35\theta+8\right)+2^{2} x^{2}\left(2277\theta^4+3252\theta^3+4573\theta^2+3266\theta+992\right)+2^{4} x^{3}\left(20907\theta^4+47634\theta^3+77375\theta^2+65724\theta+24022\right)+2^{7} x^{4}\left(62171\theta^4+199492\theta^3+375946\theta^2+371450\theta+156488\right)+2^{9} x^{5}\left(253302\theta^4+1066440\theta^3+2327568\theta^2+2630202\theta+1250623\right)+2^{10} x^{6}\left(1459436\theta^4+7698000\theta^3+19344508\theta^2+24706800\theta+13098093\right)+2^{12} x^{7}\left(3024300\theta^4+19348248\theta^3+55554208\theta^2+79484188\theta+46581901\right)+2^{15} x^{8}\left(2268548\theta^4+17191376\theta^3+55960360\theta^2+89050336\theta+57303573\right)+2^{18} x^{9}\left(1227744\theta^4+10826688\theta^3+39662704\theta^2+69775740\theta+49021017\right)+2^{20} x^{10}\left(945104\theta^4+9566080\theta^3+39177592\theta^2+75788768\theta+57836847\right)+2^{22} x^{11}\left(502368\theta^4+5772864\theta^3+26266668\theta^2+55590540\theta+45853745\right)+2^{25} x^{12}\left(87264\theta^4+1128192\theta^3+5668024\theta^2+13052400\theta+11573495\right)+2^{30} 5 x^{13}\left(444\theta^4+6408\theta^3+35315\theta^2+87905\theta+83203\right)+2^{35} 5^{2} x^{14}\left((\theta+4)^4\right)\)

Maple LaTex

Coefficients of the holomorphic solution: 1, -16, 196, -2352, 29920, ...
--> OEIS
Normalized instanton numbers (n₀=1): 2, -29/4, 38, -2077/8, 2034, ... ; Common denominator:...

Discriminant

$(4z+1)(2z+1)^2(64z^2+24z+1)^2(160z^2+32z+1)^2(8z+1)^3$

Local exponents

$-\frac{ 1}{ 2}$ $-\frac{ 3}{ 16}-\frac{ 1}{ 16}\sqrt{ 5}$ $-\frac{ 1}{ 4}$ $-\frac{ 1}{ 10}-\frac{ 1}{ 40}\sqrt{ 6}$ $-\frac{ 1}{ 8}$ $-\frac{ 3}{ 16}+\frac{ 1}{ 16}\sqrt{ 5}$ $-\frac{ 1}{ 10}+\frac{ 1}{ 40}\sqrt{ 6}$ $0$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $4$
$1$ $\frac{ 1}{ 2}$ $1$ $1$ $0$ $\frac{ 1}{ 2}$ $1$ $0$ $4$
$-2$ $\frac{ 1}{ 2}$ $1$ $3$ $0$ $\frac{ 1}{ 2}$ $3$ $0$ $4$
$3$ $1$ $2$ $4$ $0$ $1$ $4$ $0$ $4$

\(-\frac{ 1}{ 2}\)	\(-\frac{ 3}{ 16}-\frac{ 1}{ 16}\sqrt{ 5}\)	\(-\frac{ 1}{ 4}\)	\(-\frac{ 1}{ 10}-\frac{ 1}{ 40}\sqrt{ 6}\)	\(-\frac{ 1}{ 8}\)	\(-\frac{ 3}{ 16}+\frac{ 1}{ 16}\sqrt{ 5}\)	\(-\frac{ 1}{ 10}+\frac{ 1}{ 40}\sqrt{ 6}\)	\(0\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(4\)
\(1\)	\(\frac{ 1}{ 2}\)	\(1\)	\(1\)	\(0\)	\(\frac{ 1}{ 2}\)	\(1\)	\(0\)	\(4\)
\(-2\)	\(\frac{ 1}{ 2}\)	\(1\)	\(3\)	\(0\)	\(\frac{ 1}{ 2}\)	\(3\)	\(0\)	\(4\)
\(3\)	\(1\)	\(2\)	\(4\)	\(0\)	\(1\)	\(4\)	\(0\)	\(4\)

Note:

This is operator "14.10" from ...

9

New Number: 15.2 | AESZ: | Superseeker: 2 38 | Hash: 76d5c5e186c39f14d8f32dfa0f13e22a

Degree: 15

\(\theta^4+2 x\left(73\theta^4+40\theta^3+47\theta^2+27\theta+6\right)+2^{2} x^{2}\left(2349\theta^4+2724\theta^3+3516\theta^2+2273\theta+614\right)+2^{3} x^{3}\left(44091\theta^4+80304\theta^3+115043\theta^2+84574\theta+26356\right)+2^{5} x^{4}\left(269591\theta^4+678346\theta^3+1084179\theta^2+893856\theta+309842\right)+2^{8} x^{5}\left(568775\theta^4+1835004\theta^3+3266314\theta^2+2971734\theta+1120498\right)+2^{11} x^{6}\left(856369\theta^4+3369012\theta^3+6631886\theta^2+6564309\theta+2651780\right)+2^{11} x^{7}\left(7508036\theta^4+34719008\theta^3+74840604\theta^2+79593816\theta+34039943\right)+2^{13} x^{8}\left(12098492\theta^4+63919352\theta^3+149239952\theta^2+168641212\theta+75569097\right)+2^{16} x^{9}\left(7179524\theta^4+42349744\theta^3+105902696\theta^2+125838704\theta+58525593\right)+2^{19} x^{10}\left(3117952\theta^4+20136896\theta^3+53326176\theta^2+65967996\theta+31556287\right)+2^{21} x^{11}\left(1949840\theta^4+13550976\theta^3+37571920\theta^2+47915544\theta+23371681\right)+2^{23} x^{12}\left(851424\theta^4+6266688\theta^3+17985676\theta^2+23424156\theta+11560933\right)+2^{26} x^{13}\left(122784\theta^4+942720\theta^3+2770088\theta^2+3654240\theta+1815239\right)+2^{31} 5 x^{14}\left(524\theta^4+4136\theta^3+12323\theta^2+16373\theta+8173\right)+2^{36} 5^{2} x^{15}\left((\theta+2)^4\right)\)

Maple LaTex

Coefficients of the holomorphic solution: 1, -12, 136, -1632, 21296, ...
--> OEIS
Normalized instanton numbers (n₀=1): 2, -29/4, 38, -2077/8, 2034, ... ; Common denominator:...

Discriminant

$(4z+1)(64z^2+24z+1)^2(160z^2+32z+1)^2(2z+1)^3(8z+1)^3$

Local exponents

$-\frac{ 1}{ 2}$ $-\frac{ 3}{ 16}-\frac{ 1}{ 16}\sqrt{ 5}$ $-\frac{ 1}{ 4}$ $-\frac{ 1}{ 10}-\frac{ 1}{ 40}\sqrt{ 6}$ $-\frac{ 1}{ 8}$ $-\frac{ 3}{ 16}+\frac{ 1}{ 16}\sqrt{ 5}$ $-\frac{ 1}{ 10}+\frac{ 1}{ 40}\sqrt{ 6}$ $0$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $2$
$2$ $\frac{ 1}{ 2}$ $1$ $1$ $0$ $\frac{ 1}{ 2}$ $1$ $0$ $2$
$3$ $\frac{ 1}{ 2}$ $1$ $3$ $0$ $\frac{ 1}{ 2}$ $3$ $0$ $2$
$5$ $1$ $2$ $4$ $0$ $1$ $4$ $0$ $2$

\(-\frac{ 1}{ 2}\)	\(-\frac{ 3}{ 16}-\frac{ 1}{ 16}\sqrt{ 5}\)	\(-\frac{ 1}{ 4}\)	\(-\frac{ 1}{ 10}-\frac{ 1}{ 40}\sqrt{ 6}\)	\(-\frac{ 1}{ 8}\)	\(-\frac{ 3}{ 16}+\frac{ 1}{ 16}\sqrt{ 5}\)	\(-\frac{ 1}{ 10}+\frac{ 1}{ 40}\sqrt{ 6}\)	\(0\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(2\)
\(2\)	\(\frac{ 1}{ 2}\)	\(1\)	\(1\)	\(0\)	\(\frac{ 1}{ 2}\)	\(1\)	\(0\)	\(2\)
\(3\)	\(\frac{ 1}{ 2}\)	\(1\)	\(3\)	\(0\)	\(\frac{ 1}{ 2}\)	\(3\)	\(0\)	\(2\)
\(5\)	\(1\)	\(2\)	\(4\)	\(0\)	\(1\)	\(4\)	\(0\)	\(2\)

Note:

This is operator "15.2" from ...

10

New Number: 6.17 | AESZ: | Superseeker: 2 224/9 | Hash: bbcabbebf6c04783d4ec5d0a5664f174

Degree: 6

$\theta^4-x\left(14+73\theta+154\theta^2+162\theta^3+81\theta^4\right)+x^{2}\left(3256+11390\theta+15571\theta^2+9876\theta^3+2469\theta^4\right)-x^{3}\left(162708+457536\theta+476503\theta^2+215994\theta^3+35999\theta^4\right)+2 3 5 x^{4}\left(8837\theta^4+70696\theta^3+200535\theta^2+236572\theta+98316\right)-2^{2} 3^{2} 5^{2} 7 x^{5}(\theta+4)(\theta+1)(151\theta^2+755\theta+850)+2^{3} 3^{3} 5^{3} 7^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 14, 220, 3800, 70840, ...
--> OEIS
Normalized instanton numbers (n₀=1): 2, -4, 224/9, -112, 4446/5, ... ; Common denominator:...

Discriminant

$(6z-1)(14z-1)(30z-1)(21z-1)(-1+5z)^2$

Local exponents

$0$ $\frac{ 1}{ 30}$ $\frac{ 1}{ 21}$ $\frac{ 1}{ 14}$ $\frac{ 1}{ 6}$ $\frac{ 1}{ 5}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $1$
$0$ $1$ $1$ $1$ $1$ $\frac{ 1}{ 2}$ $2$
$0$ $1$ $1$ $1$ $1$ $\frac{ 1}{ 2}$ $4$
$0$ $2$ $2$ $2$ $2$ $1$ $5$

\(0\)	\(\frac{ 1}{ 30}\)	\(\frac{ 1}{ 21}\)	\(\frac{ 1}{ 14}\)	\(\frac{ 1}{ 6}\)	\(\frac{ 1}{ 5}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)	\(2\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)	\(4\)
\(0\)	\(2\)	\(2\)	\(2\)	\(2\)	\(1\)	\(5\)

Note:

This is operator "6.17" from ...

11

New Number: 6.38 | AESZ: | Superseeker: 2 952 | Hash: ab13475ec61ba4278f6e59d858b5c527

Degree: 6

$\theta^4-2 x\left(84\theta^4+264\theta^3+299\theta^2+167\theta+37\right)+2^{2} x^{2}\left(260\theta^4+10640\theta^3+22443\theta^2+18950\theta+6071\right)+2^{7} x^{3}\left(4550\theta^4+16140\theta^3+7327\theta^2-8178\theta-6485\right)+2^{12} x^{4}\left(935\theta^4-8660\theta^3-28587\theta^2-29234\theta-10036\right)-2^{18} 3 x^{5}\left(414\theta^4+2385\theta^3+5123\theta^2+4909\theta+1773\right)-2^{22} 3^{2} x^{6}(3\theta+5)^2(3\theta+4)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 74, 6354, 585020, 55958290, ...
--> OEIS
Normalized instanton numbers (n₀=1): 2, -172, 952, -45148, 17303644/25, ... ; Common denominator:...

Discriminant

$-(-1+16z+256z^2)(32z+1)^2(108z-1)^2$

Local exponents

$-\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}$ $-\frac{ 1}{ 32}$ $0$ $\frac{ 1}{ 108}$ $-\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 4}{ 3}$
$1$ $1$ $0$ $-\frac{ 1}{ 2}$ $1$ $\frac{ 4}{ 3}$
$1$ $3$ $0$ $1$ $1$ $\frac{ 5}{ 3}$
$2$ $4$ $0$ $\frac{ 3}{ 2}$ $2$ $\frac{ 5}{ 3}$

\(-\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\)	\(-\frac{ 1}{ 32}\)	\(0\)	\(\frac{ 1}{ 108}\)	\(-\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 4}{ 3}\)
\(1\)	\(1\)	\(0\)	\(-\frac{ 1}{ 2}\)	\(1\)	\(\frac{ 4}{ 3}\)
\(1\)	\(3\)	\(0\)	\(1\)	\(1\)	\(\frac{ 5}{ 3}\)
\(2\)	\(4\)	\(0\)	\(\frac{ 3}{ 2}\)	\(2\)	\(\frac{ 5}{ 3}\)

Note:

This is operator "6.38" from ...

12

New Number: 8.54 | AESZ: | Superseeker: 0 1/3 | Hash: bb80872017d0578a4ae56172666b807c

Degree: 8

$\theta^4+x\theta(3\theta^3-6\theta^2-4\theta-1)-x^{2}\left(211\theta^4+856\theta^3+1433\theta^2+1184\theta+384\right)-2 x^{3}\left(761\theta^4+3288\theta^3+6477\theta^2+6654\theta+2700\right)+2^{2} x^{4}(\theta+1)(2013\theta^3+17379\theta^2+40726\theta+28548)+2^{3} x^{5}(\theta+1)(15719\theta^3+126105\theta^2+325408\theta+269508)+2^{5} 3^{2} x^{6}(\theta+1)(\theta+2)(1817\theta^2+11967\theta+19631)+2^{7} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(89\theta+350)+2^{9} 3^{3} 43 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 0, 24, 72, 1296, ...
--> OEIS
Normalized instanton numbers (n₀=1): 0, 1/2, 1/3, -1, 2, ... ; Common denominator:...

Discriminant

$(4z+1)(6z+1)(43z^2+13z+1)(2z+1)^2(12z-1)^2$

Local exponents

$-\frac{ 1}{ 2}$ $-\frac{ 1}{ 4}$ $-\frac{ 1}{ 6}$ $-\frac{ 13}{ 86}-\frac{ 1}{ 86}\sqrt{ 3}I$ $-\frac{ 13}{ 86}+\frac{ 1}{ 86}\sqrt{ 3}I$ $0$ $\frac{ 1}{ 12}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $1$
$1$ $1$ $1$ $1$ $1$ $0$ $\frac{ 1}{ 2}$ $2$
$3$ $1$ $1$ $1$ $1$ $0$ $\frac{ 1}{ 2}$ $3$
$4$ $2$ $2$ $2$ $2$ $0$ $1$ $4$

\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 4}\)	\(-\frac{ 1}{ 6}\)	\(-\frac{ 13}{ 86}-\frac{ 1}{ 86}\sqrt{ 3}I\)	\(-\frac{ 13}{ 86}+\frac{ 1}{ 86}\sqrt{ 3}I\)	\(0\)	\(\frac{ 1}{ 12}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(0\)	\(\frac{ 1}{ 2}\)	\(2\)
\(3\)	\(1\)	\(1\)	\(1\)	\(1\)	\(0\)	\(\frac{ 1}{ 2}\)	\(3\)
\(4\)	\(2\)	\(2\)	\(2\)	\(2\)	\(0\)	\(1\)	\(4\)

Note:

This is operator "8.54" from ...

13

New Number: 6.35 | AESZ: | Superseeker: 2 224/9 | Hash: 31d226ff68f616edaab012f85462b8e9

Degree: 6

$\theta^4-x\left(9+48\theta+104\theta^2+112\theta^3+41\theta^4\right)+2 x^{2}\left(167\theta^4+1358\theta^3+2593\theta^2+1990\theta+573\right)+2 x^{3}\left(1273\theta^4-822\theta^3-16239\theta^2-22188\theta-9009\right)-5 x^{4}\left(3923\theta^4+29740\theta^3+51878\theta^2+33360\theta+6534\right)-5^{2} x^{5}(\theta+1)(2929\theta^3+4467\theta^2-1969\theta-4047)+2^{2} 3^{2} 5^{4} x^{6}(\theta+2)(\theta+1)(2\theta+3)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 9, 105, 1425, 21465, ...
--> OEIS
Normalized instanton numbers (n₀=1): 2, -4, 224/9, -112, 4446/5, ... ; Common denominator:...

Discriminant

No data for singularities

Note:

This is operator "6.35" from ...

\(.924152876+.943952044I\)	\(.188111204+1.275393351I\)	\(.593885779-.164736576I\)	\(-.98788356e-1-.111719004I\)
\(.205812544+3.214663066I\)	\(2.256285526+4.201440782I\)	\(1.918711704-.844672672I\)	\(-.387126151-.327818207I\)
\(-.81202836e-1+5.639775328I\)	\(1.617313859+7.506248400I\)	\(4.465075410-1.211574339I\)	\(-.630856884-.62528948587308939323761000463177396943029180176007410838351088466882816118573413617415470125057897174617878647522000926354793886058360352014821676702176933765632237146827234830940250115794349235757295I\)
\(2.469750531+38.575956789I\)	\(15.075426310+50.417289384I\)	\(23.024540442-10.136072063I\)	\(-3.645513812-3.933818487I\)

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

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

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

\(.16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667+.969204490I\)	\(-\frac{ 1}{ 12}+20\lambda\)	\(-\frac{ 1}{ 18}+\frac{ 40}{ 3}\lambda\)	\(.2449129e-2+\frac{ 10}{ 3}\lambda\)
\(\frac{ 20}{ 3}\)	\(\frac{ 5}{ 3}\)	\(\frac{ 4}{ 9}\)	\(\frac{ 1}{ 18}-\frac{ 40}{ 3}\lambda\)
\(-10\)	\(-1\)	\(\frac{ 1}{ 3}\)	\(-\frac{ 1}{ 12}+20\lambda\)
\(100\)	\(10\)	\(\frac{ 20}{ 3}\)	\(1.8333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-.969204490I\)

\(1+16\lambda\)	\(0\)	\(\frac{ 4}{ 3}\lambda\)	\(.125248e-3\)
\(4\)	\(1\)	\(\frac{ 1}{ 3}\)	\(-\frac{ 4}{ 3}\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(48\)	\(0\)	\(4\)	\(1-16\lambda\)

\(-16\lambda\)	\(12\)	\(1\)	\(1\)
\(-4\)	\(-24\)	\(-1\)	\(0\)
\(0\)	\(48\)	\(0\)	\(0\)
\(-48\)	\(0\)	\(0\)	\(0\)

\(1.8333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333+.969204490I\)	\(-\frac{ 1}{ 12}-20\lambda\)	\(\frac{ 1}{ 18}+\frac{ 40}{ 3}\lambda\)	\(.2449129e-2-\frac{ 10}{ 3}\lambda\)
\(\frac{ 20}{ 3}\)	\(\frac{ 1}{ 3}\)	\(\frac{ 4}{ 9}\)	\(-\frac{ 1}{ 18}-\frac{ 40}{ 3}\lambda\)
\(10\)	\(-1\)	\(\frac{ 5}{ 3}\)	\(-\frac{ 1}{ 12}-20\lambda\)
\(100\)	\(-10\)	\(\frac{ 20}{ 3}\)	\(.16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667-.969204490I\)

\(\frac{ 5}{ 6}-\frac{ 96920449}{ 100000000}I\)	\(\frac{ 85}{ 3}\)	\(\frac{ 11}{ 10}\)	\(1\)
\(-\frac{ 20}{ 3}\)	\(-60\)	\(-1\)	\(0\)
\(10\)	\(100\)	\(0\)	\(0\)
\(-100\)	\(0\)	\(0\)	\(0\)

\(-80\lambda\)	\(25\)	\(1\)	\(1\)
\(-5\)	\(-60\)	\(-1\)	\(0\)
\(0\)	\(120\)	\(0\)	\(0\)
\(-120\)	\(0\)	\(0\)	\(0\)

Calabi-Yau differential operator database v.3

Summary

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

Discriminant

Local exponents

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

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

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice