Calabi-Yau differential operator database v.3.0

1

New Number: 2.53 | AESZ: 29 | Superseeker: 14 10424/3 | Hash: 92e8a038051b3fb8e0cc6ad6a52b8bfb

Degree: 2

$\theta^4-2 x(2\theta+1)^2(17\theta^2+17\theta+5)+2^{2} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)$

Coefficients of the holomorphic solution: 1, 10, 438, 28900, 2310070, ...
--> OEIS
Normalized instanton numbers (n₀=1): 14, 303/2, 10424/3, 113664, 4579068, ... ; Common denominator:...

Discriminant

$1-136z+16z^2$

Local exponents

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

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

Note:

Hadamard product $I \ast \gamma$

	Gopakumar-Vafa invariants
g=0	336, 3636, 83392, 2727936, 109897632, 5057935376, 255380668896, 13802556520272,...
g=1	0, 0, 0, 66, 121056, 29099400, 4233172704, 496392888006,...
g=2	,...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-116\)	\(72\)	\(24\)	\(10\)

2

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

3

New Number: 5.70 | AESZ: 287 | Superseeker: 361/21 120472/21 | Hash: 97932196c46a8712f6dcb11165d698be

Degree: 5

$3^{2} 7^{2} \theta^4-3 7 x\left(3289\theta^4+6098\theta^3+4645\theta^2+1596\theta+210\right)+2^{2} 5 x^{2}\left(7712\theta^4-46168\theta^3-106885\theta^2-67410\theta-13629\right)+2^{4} x^{3}\left(106636\theta^4+493416\theta^3+420211\theta^2+116361\theta+6090\right)-2^{8} 5 x^{4}(2\theta+1)(1916\theta^3+2622\theta^2+1077\theta+91)-2^{12} 5^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 10, 510, 38260, 3473470, ...
--> OEIS
Normalized instanton numbers (n₀=1): 361/21, 4780/21, 120472/21, 1537864/7, 216261320/21, ... ; Common denominator:...

Discriminant

$-(64z^3+800z^2+149z-1)(-21+80z)^2$

Local exponents

≈$-12.310784$ ≈$-0.195701$ $0$ ≈$0.006485$ $\frac{ 21}{ 80}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $0$ $1$ $1$ $1$
$1$ $1$ $0$ $1$ $3$ $1$
$2$ $2$ $0$ $2$ $4$ $\frac{ 3}{ 2}$

≈\(-12.310784\)	≈\(-0.195701\)	\(0\)	≈\(0.006485\)	\(\frac{ 21}{ 80}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)
\(1\)	\(1\)	\(0\)	\(1\)	\(3\)	\(1\)
\(2\)	\(2\)	\(0\)	\(2\)	\(4\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.70" from ...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-104\)	\(66\)	\(21\)	\(9\)

4

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

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

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

Note:

This is operator "5.79" from ...

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

5

New Number: 10.8 | AESZ: | Superseeker: 7 -2044/9 | Hash: 772d055ae4c1a5d6a65a2b1f3ffa351b

Degree: 10

$\theta^4-x\left(147\theta^2+10+60\theta+174\theta^3+111\theta^4\right)+2^{2} x^{2}\left(1269\theta^4+3576\theta^3+4595\theta^2+2722\theta+639\right)-2^{2} x^{3}\left(28236\theta^4+92256\theta^3+135641\theta^2+100407\theta+29996\right)+2^{4} 3 x^{4}\left(34932\theta^4+117280\theta^3+166025\theta^2+128238\theta+41467\right)-2^{6} x^{5}\left(266139\theta^4+937698\theta^3+1398643\theta^2+1056533\theta+325061\right)+2^{8} x^{6}\left(478785\theta^4+1758504\theta^3+2952901\theta^2+2388960\theta+754208\right)-2^{8} x^{7}\left(2371176\theta^4+9770640\theta^3+17775969\theta^2+15468753\theta+5209610\right)+2^{10} x^{8}\left(1853604\theta^4+9368112\theta^3+18957629\theta^2+17669710\theta+6248237\right)-2^{12} 11 x^{9}(2\theta+3)(36502\theta^3+178659\theta^2+286703\theta+145866)+2^{16} 3 5^{2} 11^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 10, 154, 2548, 27370, ...
--> OEIS
Normalized instanton numbers (n₀=1): 7, -31/4, -2044/9, -1380, -8520, ... ; Common denominator:...

Discriminant

$(3z-1)(6400z^3-2352z^2+84z-1)(4z-1)^2(88z^2-8z+1)^2$

Local exponents

$0$ ≈$0.019222-0.010265I$ ≈$0.019222+0.010265I$ $\frac{ 1}{ 22}-\frac{ 3}{ 44}\sqrt{ 2}I$ $\frac{ 1}{ 22}+\frac{ 3}{ 44}\sqrt{ 2}I$ $\frac{ 1}{ 4}$ ≈$0.329056$ $\frac{ 1}{ 3}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $1$
$0$ $1$ $1$ $1$ $1$ $\frac{ 1}{ 2}$ $1$ $1$ $\frac{ 3}{ 2}$
$0$ $1$ $1$ $3$ $3$ $\frac{ 1}{ 2}$ $1$ $1$ $\frac{ 5}{ 2}$
$0$ $2$ $2$ $4$ $4$ $1$ $2$ $2$ $3$

\(0\)	≈\(0.019222-0.010265I\)	≈\(0.019222+0.010265I\)	\(\frac{ 1}{ 22}-\frac{ 3}{ 44}\sqrt{ 2}I\)	\(\frac{ 1}{ 22}+\frac{ 3}{ 44}\sqrt{ 2}I\)	\(\frac{ 1}{ 4}\)	≈\(0.329056\)	\(\frac{ 1}{ 3}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)	\(1\)	\(1\)	\(\frac{ 3}{ 2}\)
\(0\)	\(1\)	\(1\)	\(3\)	\(3\)	\(\frac{ 1}{ 2}\)	\(1\)	\(1\)	\(\frac{ 5}{ 2}\)
\(0\)	\(2\)	\(2\)	\(4\)	\(4\)	\(1\)	\(2\)	\(2\)	\(3\)

Note:

This is operator "10.8" from ...

6

New Number: 13.16 | AESZ: | Superseeker: 5 581/3 | Hash: 2ab5512d2cfda3cde6ee0ea98a12d6fb

Degree: 13

\(\theta^4-x\left(106\theta^4+140\theta^3+125\theta^2+55\theta+10\right)+x^{2}\left(2472+4265\theta^4+12596\theta^3+15925\theta^2+9718\theta\right)-2^{3} x^{3}\left(9346\theta^4+58443\theta^3+105118\theta^2+80373\theta+24412\right)+2^{4} 3 x^{4}\left(1747\theta^4+173306\theta^3+488163\theta^2+460544\theta+161900\right)+2^{6} 3 x^{5}\left(108841\theta^4-198029\theta^3-1835967\theta^2-2248271\theta-919518\right)-2^{8} 3 x^{6}\left(510411\theta^4+1710438\theta^3-2652339\theta^2-5816622\theta-2956384\right)+2^{12} 3 x^{7}\left(213944\theta^4+2327365\theta^3+1622852\theta^2-837189\theta-1027734\right)+2^{10} 3 x^{8}\left(4640003\theta^4-76516006\theta^3-140342311\theta^2-92680566\theta-16297224\right)-2^{13} x^{9}\left(56543147\theta^4-21416544\theta^3-251991507\theta^2-314165376\theta-118113840\right)+2^{16} x^{10}\left(70691941\theta^4+213840362\theta^3+253613996\theta^2+121602823\theta+15102754\right)-2^{19} 73 x^{11}(\theta+1)(680053\theta^3+2794143\theta^2+4238129\theta+2311527)+2^{22} 73^{2} x^{12}(\theta+2)(\theta+1)(3707\theta^2+13713\theta+13693)-2^{25} 3^{2} 73^{3} x^{13}(\theta+1)(\theta+2)^2(\theta+3)\)

Maple LaTex

Coefficients of the holomorphic solution: 1, 10, 118, 1864, 38566, ...
--> OEIS
Normalized instanton numbers (n₀=1): 5, -53/4, 581/3, -1231, 19810, ... ; Common denominator:...

Discriminant

$-(9z-1)(8z-1)(4672z^3-840z^2+57z-1)(64z^2-8z+1)(1-12z-192z^2+2336z^3)^2$

Local exponents

≈$-0.071938$ $0$ ≈$0.026164$ $\frac{ 1}{ 16}-\frac{ 1}{ 16}\sqrt{ 3}I$ $\frac{ 1}{ 16}+\frac{ 1}{ 16}\sqrt{ 3}I$ ≈$0.076815-0.047751I$ ≈$0.076815+0.047751I$ ≈$0.077065-0.003429I$ ≈$0.077065+0.003429I$ $\frac{ 1}{ 9}$ $\frac{ 1}{ 8}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $1$
$1$ $0$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $2$
$3$ $0$ $1$ $1$ $1$ $1$ $1$ $3$ $3$ $1$ $1$ $2$
$4$ $0$ $2$ $2$ $2$ $2$ $2$ $4$ $4$ $2$ $2$ $3$

≈\(-0.071938\)	\(0\)	≈\(0.026164\)	\(\frac{ 1}{ 16}-\frac{ 1}{ 16}\sqrt{ 3}I\)	\(\frac{ 1}{ 16}+\frac{ 1}{ 16}\sqrt{ 3}I\)	≈\(0.076815-0.047751I\)	≈\(0.076815+0.047751I\)	≈\(0.077065-0.003429I\)	≈\(0.077065+0.003429I\)	\(\frac{ 1}{ 9}\)	\(\frac{ 1}{ 8}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(2\)
\(3\)	\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(3\)	\(3\)	\(1\)	\(1\)	\(2\)
\(4\)	\(0\)	\(2\)	\(2\)	\(2\)	\(2\)	\(2\)	\(4\)	\(4\)	\(2\)	\(2\)	\(3\)

Note:

This is operator "13.16" from ...

7

New Number: 6.12 | AESZ: | Superseeker: 19 2263 | Hash: 86993fb7955dee498aab7e103a0f457e

Degree: 6

$\theta^4-x\left(33\theta^4+258\theta^3+199\theta^2+70\theta+10\right)-2^{2} x^{2}\left(1380\theta^4+2400\theta^3-173\theta^2-634\theta-185\right)-2^{4} x^{3}\left(7325\theta^4+2670\theta^3-668\theta^2-1035\theta-290\right)-2^{7} x^{4}\left(897\theta^4-3504\theta^3-10058\theta^2-8492\theta-2435\right)+2^{12} x^{5}(\theta+1)^2(858\theta^2+1566\theta+745)-2^{17} 5^{2} x^{6}(\theta+1)^2(\theta+2)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 10, 310, 14860, 869590, ...
--> OEIS
Normalized instanton numbers (n₀=1): 19, -18, 2263, 4184, 1097345, ... ; Common denominator:...

Discriminant

$-(z-1)(8z+1)(100z-1)(4z-1)(1+32z)^2$

Local exponents

$-\frac{ 1}{ 8}$ $-\frac{ 1}{ 32}$ $0$ $\frac{ 1}{ 100}$ $\frac{ 1}{ 4}$ $1$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $1$
$1$ $1$ $0$ $1$ $1$ $1$ $1$
$1$ $3$ $0$ $1$ $1$ $1$ $2$
$2$ $4$ $0$ $2$ $2$ $2$ $2$

\(-\frac{ 1}{ 8}\)	\(-\frac{ 1}{ 32}\)	\(0\)	\(\frac{ 1}{ 100}\)	\(\frac{ 1}{ 4}\)	\(1\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(1\)
\(1\)	\(3\)	\(0\)	\(1\)	\(1\)	\(1\)	\(2\)
\(2\)	\(4\)	\(0\)	\(2\)	\(2\)	\(2\)	\(2\)

Note:

This is operator "6.12" from ...

8

New Number: 8.26 | AESZ: 301 | Superseeker: 193/11 48570/11 | Hash: a91db18876a9dfbf42b88f8d64c55d85

Degree: 8

$11^{2} \theta^4-11 x\left(1517\theta^4+3136\theta^3+2393\theta^2+825\theta+110\right)-x^{2}\left(24266+106953\theta+202166\theta^2+207620\theta^3+90362\theta^4\right)-x^{3}\left(53130+217437\theta+415082\theta^2+507996\theta^3+245714\theta^4\right)-x^{4}\left(15226+183269\theta+564786\theta^2+785972\theta^3+407863\theta^4\right)-x^{5}\left(25160+279826\theta+728323\theta^2+790148\theta^3+434831\theta^4\right)-2^{3} x^{6}\left(36361\theta^4+70281\theta^3+73343\theta^2+37947\theta+7644\right)-2^{4} 5 x^{7}\left(1307\theta^4+3430\theta^3+3877\theta^2+2162\theta+488\right)-2^{9} 5^{2} x^{8}\left((\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 10, 466, 32392, 2727826, ...
--> OEIS
Normalized instanton numbers (n₀=1): 193/11, 1973/11, 48570/11, 1689283/11, 72444183/11, ... ; Common denominator:...

Discriminant

$-(-1+143z+32z^2)(z+1)^2(20z^2+17z+11)^2$

Local exponents

$-\frac{ 143}{ 64}-\frac{ 19}{ 64}\sqrt{ 57}$ $-1$ $-\frac{ 17}{ 40}-\frac{ 1}{ 40}\sqrt{ 591}I$ $-\frac{ 17}{ 40}+\frac{ 1}{ 40}\sqrt{ 591}I$ $0$ $-\frac{ 143}{ 64}+\frac{ 19}{ 64}\sqrt{ 57}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $1$
$1$ $\frac{ 1}{ 2}$ $1$ $1$ $0$ $1$ $1$
$1$ $\frac{ 1}{ 2}$ $3$ $3$ $0$ $1$ $1$
$2$ $1$ $4$ $4$ $0$ $2$ $1$

\(-\frac{ 143}{ 64}-\frac{ 19}{ 64}\sqrt{ 57}\)	\(-1\)	\(-\frac{ 17}{ 40}-\frac{ 1}{ 40}\sqrt{ 591}I\)	\(-\frac{ 17}{ 40}+\frac{ 1}{ 40}\sqrt{ 591}I\)	\(0\)	\(-\frac{ 143}{ 64}+\frac{ 19}{ 64}\sqrt{ 57}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(\frac{ 1}{ 2}\)	\(1\)	\(1\)	\(0\)	\(1\)	\(1\)
\(1\)	\(\frac{ 1}{ 2}\)	\(3\)	\(3\)	\(0\)	\(1\)	\(1\)
\(2\)	\(1\)	\(4\)	\(4\)	\(0\)	\(2\)	\(1\)

Note:

This operator has a second MUM-point at infinity corresponding to operator 8.27.

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-84\)	\(64\)	\(22\)	\(9\)

9

New Number: 8.50 | AESZ: | Superseeker: 2/23 27/23 | Hash: 68499833fa99ef8841a3d64e042d4a6e

Degree: 8

$23^{2} \theta^4-2 23 x\theta^2(136\theta^2+2\theta+1)-2^{2} x^{2}\left(7589\theta^4+54926\theta^3+89975\theta^2+69828\theta+21160\right)+x^{3}\left(573259\theta^4+2342274\theta^3+3791849\theta^2+3070914\theta+1010160\right)-2 5 x^{4}\left(122351\theta^4+62266\theta^3-795547\theta^2-1404486\theta-669744\right)-2^{3} 3 5^{2} x^{5}(\theta+1)(16105\theta^3+133047\theta^2+320040\theta+245740)+2^{4} 3^{2} 5^{3} x^{6}(\theta+1)(\theta+2)(3107\theta^2+16911\theta+22834)-2^{4} 3^{4} 5^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(133\theta+404)+2^{5} 3^{6} 5^{5} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 0, 10, 0, 270, ...
--> OEIS
Normalized instanton numbers (n₀=1): 2/23, 18/23, 27/23, 136/23, 395/23, ... ; Common denominator:...

Discriminant

$(3z-1)(2z-1)(10z-1)(6z+1)(25z^2-5z-1)(-23+90z)^2$

Local exponents

$-\frac{ 1}{ 6}$ $\frac{ 1}{ 10}-\frac{ 1}{ 10}\sqrt{ 5}$ $0$ $\frac{ 1}{ 10}$ $\frac{ 23}{ 90}$ $\frac{ 1}{ 10}+\frac{ 1}{ 10}\sqrt{ 5}$ $\frac{ 1}{ 3}$ $\frac{ 1}{ 2}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $1$
$1$ $1$ $0$ $1$ $1$ $1$ $1$ $1$ $2$
$1$ $1$ $0$ $1$ $3$ $1$ $1$ $1$ $3$
$2$ $2$ $0$ $2$ $4$ $2$ $2$ $2$ $4$

\(-\frac{ 1}{ 6}\)	\(\frac{ 1}{ 10}-\frac{ 1}{ 10}\sqrt{ 5}\)	\(0\)	\(\frac{ 1}{ 10}\)	\(\frac{ 23}{ 90}\)	\(\frac{ 1}{ 10}+\frac{ 1}{ 10}\sqrt{ 5}\)	\(\frac{ 1}{ 3}\)	\(\frac{ 1}{ 2}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(2\)
\(1\)	\(1\)	\(0\)	\(1\)	\(3\)	\(1\)	\(1\)	\(1\)	\(3\)
\(2\)	\(2\)	\(0\)	\(2\)	\(4\)	\(2\)	\(2\)	\(2\)	\(4\)

Note:

This is operator "8.50" from ...

10

New Number: 24.5 | AESZ: | Superseeker: -16/5 -1867567/6075 | Hash: 2b54ac5ab682fefda99613b12639de0d

Degree: 24

\(5^{2} \theta^4-5 x\left(87\theta^4+558\theta^3+544\theta^2+265\theta+50\right)-x^{2}\left(45889\theta^4-29468\theta^3-129151\theta^2-143110\theta-44000\right)+2^{3} x^{3}\left(101735\theta^4+270942\theta^3-280942\theta^2-787035\theta-293140\right)+2^{4} x^{4}\left(1601399\theta^4-2849378\theta^3-262002\theta^2+12518815\theta+6061138\right)-2^{6} x^{5}\left(9827313\theta^4+2164410\theta^3-19797844\theta^2+54179083\theta+32156156\right)-2^{6} x^{6}\left(52966465\theta^4-188344608\theta^3+643951099\theta^2-283177632\theta-314950220\right)+2^{9} 3 x^{7}\left(135646615\theta^4-88299386\theta^3+413911992\theta^2+196600969\theta-12314550\right)-2^{12} x^{8}\left(332578151\theta^4-269779936\theta^3+660836210\theta^2+1220680818\theta+432226161\right)-2^{15} x^{9}\left(675921878\theta^4+631152696\theta^3+2353638328\theta^2+145156704\theta-444041163\right)+2^{18} x^{10}\left(1561753522\theta^4+983996600\theta^3+5945895278\theta^2+3679826182\theta+873763143\right)-2^{21} 3 x^{11}\left(238576054\theta^4-264476512\theta^3+1114167596\theta^2+1197405184\theta+582902907\right)-2^{24} 3^{2} x^{12}\left(156460502\theta^4+627455128\theta^3+1074872410\theta^2+965803970\theta+341599833\right)+2^{27} 3^{2} x^{13}\left(277041602\theta^4+1011477448\theta^3+239351296\theta^2+2719026848\theta+1263870699\right)-2^{30} 3^{3} x^{14}\left(52637104\theta^4+188421144\theta^3+483897488\theta^2+637072542\theta+341253003\right)-2^{33} 3^{4} x^{15}\left(5747912\theta^4+56489772\theta^3+174829980\theta^2+221976882\theta+104121013\right)+2^{36} 3^{4} x^{16}\left(16918876\theta^4+134059112\theta^3+430189490\theta^2+605545594\theta+319170645\right)-2^{39} 3^{5} x^{17}\left(4210518\theta^4+37730872\theta^3+132124328\theta^2+200474784\theta+112091805\right)+2^{42} 3^{6} x^{18}\left(447390\theta^4+5190184\theta^3+21400882\theta^2+36112146\theta+21721717\right)+2^{45} 3^{7} x^{19}\left(15750\theta^4-122992\theta^3-1334612\theta^2-3091192\theta-2193809\right)-2^{48} 3^{7} x^{20}\left(30606\theta^4+212088\theta^3+405914\theta^2+179122\theta-102711\right)+2^{51} 3^{8} x^{21}\left(2926\theta^4+28968\theta^3+87104\theta^2+106360\theta+45497\right)+2^{54} 3^{9} x^{22}\left(27\theta^4-616\theta^3-3223\theta^2-5290\theta-2877\right)-2^{57} 3^{10} x^{23}\left(21\theta^4+134\theta^3+332\theta^2+377\theta+165\right)+2^{60} 3^{11} x^{24}\left((\theta+2)^4\right)\)

Maple LaTex

Coefficients of the holomorphic solution: 1, 10, 78, 1336, 881193/40, ...
--> OEIS
Normalized instanton numbers (n₀=1): -16/5, 379/10, -1867567/6075, 1930939249/288000, -783587875717/5859375, ... ; Common denominator:...

Discriminant

$(8z+1)(64z^2-8z-1)(331776z^6-165888z^5+31104z^4-3168z^3+81z^2+35z-1)(8z-1)^2(36864z^5-4608z^4-4416z^3+1256z^2-136z+5)^2(24z+1)^3$

No data for singularities

Note:

This is operator "24.5" from ...

11

New Number: 24.8 | AESZ: | Superseeker: 22/3 35165/81 | Hash: a55f1afcd10458bac8b9d9c275171011

Degree: 24

\(3^{3} \theta^4-3^{2} x\left(219\theta^4+374\theta^3+342\theta^2+155\theta+30\right)+3 x^{2}\left(8715\theta^4+82828\theta^3+113675\theta^2+68702\theta+18336\right)+2^{3} x^{3}\left(23974\theta^4-629914\theta^3-1795354\theta^2-1328249\theta-417252\right)-2^{4} x^{4}\left(5205555\theta^4+5099190\theta^3-19218986\theta^2-17848213\theta-6421110\right)+2^{6} x^{5}\left(13128703\theta^4+84859734\theta^3-6928550\theta^2-9050837\theta-38892108\right)+2^{6} x^{6}\left(373177657\theta^4-1468788832\theta^3+1253890595\theta^2+1956928576\theta+956763572\right)-2^{9} x^{7}\left(1688667811\theta^4-1112919962\theta^3+3037312026\theta^2+4371677095\theta+2210729039\right)+2^{12} x^{8}\left(2662679451\theta^4-255238536\theta^3+2538092342\theta^2+3811548030\theta+2128293765\right)-2^{15} x^{9}\left(953791122\theta^4-3960245472\theta^3-9075894672\theta^2-9052909620\theta-3413708141\right)-2^{18} x^{10}\left(3043951122\theta^4+13172197920\theta^3+29623696538\theta^2+30862971586\theta+12758725911\right)+2^{21} x^{11}\left(4763496210\theta^4+15821276280\theta^3+31984211728\theta^2+31247157648\theta+12262706725\right)-2^{24} x^{12}\left(1682795498\theta^4+2400347728\theta^3-2355650534\theta^2-10674138478\theta-7900949901\right)-2^{27} x^{13}\left(2193574746\theta^4+13880543424\theta^3+42005217848\theta^2+59881527604\theta+32688761243\right)+2^{30} x^{14}\left(2448319808\theta^4+14353869504\theta^3+42688146876\theta^2+63027644670\theta+36405012289\right)-2^{33} x^{15}\left(377925716\theta^4+2863232932\theta^3+10986923404\theta^2+21677497070\theta+15771297495\right)-2^{36} x^{16}\left(706556068\theta^4+4516047232\theta^3+13146097430\theta^2+16807977206\theta+7656657657\right)+2^{39} 3 x^{17}\left(134822030\theta^4+1171800288\theta^3+4420283552\theta^2+7617370500\theta+4788133925\right)+2^{42} 3^{2} x^{18}\left(1459810\theta^4-50032288\theta^3-387134278\theta^2-993008390\theta-791017029\right)-2^{45} 3^{2} x^{19}\left(8666834\theta^4+64412360\theta^3+161580112\theta^2+88320472\theta-56754879\right)+2^{48} 3^{3} x^{20}\left(753758\theta^4+9752016\theta^3+38809382\theta^2+54457710\theta+23423189\right)+2^{51} 3^{4} x^{21}\left(56362\theta^4+178832\theta^3-543496\theta^2-1653284\theta-947985\right)-2^{54} 3^{4} x^{22}\left(3732\theta^4+364960\theta^3+1135967\theta^2+1505510\theta+747681\right)+2^{57} 3^{6} 5 x^{23}\left(19\theta^4+546\theta^3+2398\theta^2+3873\theta+2173\right)+2^{60} 3^{8} 5^{2} x^{24}\left((\theta+2)^4\right)\)

Maple LaTex

Coefficients of the holomorphic solution: 1, 10, 106, 1096, 1867871/144, ...
--> OEIS
Normalized instanton numbers (n₀=1): 22/3, -775/18, 35165/81, -209072675/124416, 26536592913691/182250000, ... ; Common denominator:...

Discriminant

$27-1971z-5445608554228327907328z^22+9980697350193398415360z^23+189107949793138075238400z^24+23883370048z^6-864597919232z^7+10906335031296z^8-31253827485696z^9-797953522925568z^10-48554163277605634048z^16+222357584498047057920z^17+26145z^2+191792z^3-83288880z^4+840236992z^5+57782810496372572160z^18+9989775603793920z^11-28232623553773568z^12-294416618606297088z^13+2628863376377249792z^14-3246357181074767872z^15-2744434010593261780992z^19+5728428418377707421696z^20+10280191229013163769856z^21$

No data for singularities

Note:

This is operator "24.8" from ...

\(21.+14.053465106I\)	\(-8.-5.621386042I\)	\(\frac{ 5}{ 2}+\frac{ 725}{ 2}\lambda\)	\(-.337500198-\frac{ 580}{ 3}\lambda\)
\(75\)	\(-29\)	\(\frac{ 75}{ 8}\)	\(-\frac{ 5}{ 2}-\frac{ 725}{ 2}\lambda\)
\(240\)	\(-96\)	\(31\)	\(-8.-5.621386042I\)
\(600+\frac{ 1}{ 1000000000}I\)	\(-240\)	\(75\)	\(-19.-14.053465106I\)

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

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

\(1+116\lambda\)	\(0\)	\(\frac{ 29}{ 2}\lambda\)	\(\frac{ 79}{ 6000}\)
\(3\)	\(1\)	\(\frac{ 3}{ 8}\)	\(-\frac{ 29}{ 2}\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(24\)	\(0\)	\(3\)	\(1-116\lambda\)

\(-116\lambda\)	\(7\)	\(1\)	\(1\)
\(-3\)	\(-12\)	\(-1\)	\(0\)
\(0\)	\(24\)	\(0\)	\(0\)
\(-24\)	\(0\)	\(0\)	\(0\)

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

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:

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

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

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