Calabi-Yau differential operator database v.3.0

1

New Number: 2.58 | AESZ: 46 | Superseeker: -6 -104 | Hash: 2226ec115674e71c483ba2c0350e8adf

Degree: 2

$\theta^4-2 3 x(2\theta+1)^2(9\theta^2+9\theta+5)+2^{2} 3^{6} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)$

Coefficients of the holomorphic solution: 1, 30, 1782, 129900, 10463670, ...
--> OEIS
Normalized instanton numbers (n₀=1): -6, -6, -104, 36, -4812, ... ; Common denominator:...

Discriminant

$(108z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 108}$ $\infty$
$0$ $0$ $\frac{ 1}{ 2}$
$0$ $\frac{ 1}{ 6}$ $1$
$0$ $\frac{ 5}{ 6}$ $1$
$0$ $1$ $\frac{ 3}{ 2}$

\(0\)	\(\frac{ 1}{ 108}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(\frac{ 1}{ 6}\)	\(1\)
\(0\)	\(\frac{ 5}{ 6}\)	\(1\)
\(0\)	\(1\)	\(\frac{ 3}{ 2}\)

Note:

Hadamard product $I \ast \iota$

2

New Number: 2.67 | AESZ: 245 | Superseeker: -6 -170 | Hash: 0ef0bca0dbecbedad92696fd7c0f9e42

Degree: 2

$\theta^4-2 3 x\left(36\theta^4+66\theta^3+61\theta^2+28\theta+5\right)+2^{2} 3^{2} x^{2}(3\theta+2)^2(6\theta+7)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 30, 1764, 127776, 10248750, ...
--> OEIS
Normalized instanton numbers (n₀=1): -6, -33, -170, -1029, -3246, ... ; Common denominator:...

Discriminant

$(108z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 108}$ $\infty$
$0$ $0$ $\frac{ 2}{ 3}$
$0$ $\frac{ 1}{ 6}$ $\frac{ 2}{ 3}$
$0$ $1$ $\frac{ 7}{ 6}$
$0$ $\frac{ 7}{ 6}$ $\frac{ 7}{ 6}$

\(0\)	\(\frac{ 1}{ 108}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 2}{ 3}\)
\(0\)	\(\frac{ 1}{ 6}\)	\(\frac{ 2}{ 3}\)
\(0\)	\(1\)	\(\frac{ 7}{ 6}\)
\(0\)	\(\frac{ 7}{ 6}\)	\(\frac{ 7}{ 6}\)

Note:

This is operator "2.67" from ...

Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, -6, -270, -4596, -66126, -405756, 8587836, 424349304,...
Coefficients of the q-coordinate : 0, 1, -48, 1440, -32848, 637872, -11009952, 174295160,...

	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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$1.052168056+.90357723e-1I$	$\frac{ 1}{ 4}-\frac{ 1}{ 12}I\sqrt{ 3}$	$-33^{ \frac{ 1}{ 6}}Pi^{ \frac{ 9}{ 2}}Zeta(5)^6-6\lambda$	$.10688274e-1-\frac{ 1}{ 5}I5^{ \frac{ 4}{ 7}}ln(2)^12$
$\frac{ 3}{ 2}-\frac{ 1}{ 2}I\sqrt{ 3}$	$\frac{ 3}{ 4}-\frac{ 1}{ 4}I\sqrt{ 3}$	$-\frac{ 1}{ 8}+\frac{ 1}{ 24}I\sqrt{ 3}$	$33^{ \frac{ 1}{ 6}}Pi^{ \frac{ 9}{ 2}}Zeta(5)^6+6\lambda$
$0$	$\frac{ 9}{ 2}-\frac{ 3}{ 2}I\sqrt{ 3}$	$\frac{ 3}{ 4}-\frac{ 1}{ 4}I\sqrt{ 3}$	$\frac{ 1}{ 4}-\frac{ 1}{ 12}I\sqrt{ 3}$
$-27+9I\sqrt{ 3}$	$0$	$\frac{ 3}{ 2}-\frac{ 1}{ 2}I\sqrt{ 3}$	$.447831944-.956383127I$

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Basis of the Doran-Morgan lattice

$-\frac{ 6521007}{ 125000000}-\frac{ 90357723}{ 1000000000}I$	$-3+\frac{ 4511615154067544842086723740124334848694351954431101272196462779644508392806538050844596873167533211}{ 2604782223680891931509451724762066519358428478691519147090699072692122550847025398588836869330367971}I$	$\frac{ 1}{ 2}-\frac{ 3081490456277555159153769728602633601692409347626414678367139999430219011336903561652776870289659281}{ 3558198688874218386798087732443200684026390216561310209643580926168315471826781724716716871248950591}I$	$1$
$-\frac{ 3}{ 2}+\frac{ 1}{ 2}I\sqrt{ 3}$	$\frac{ 27}{ 2}-\frac{ 5941739851857534525019677751646036095696294561235787866025785559858797774276172540036416876045407141}{ 762325578427705482137746574067229488156369299800529597635468373844463859062368874404292289563613477}I$	$-\frac{ 1}{ 2}+\frac{ 3081490456277555159153769728602633601692409347626414678367139999430219011336903561652776870289659281}{ 3558198688874218386798087732443200684026390216561310209643580926168315471826781724716716871248950591}I$	$0$
$0$	$-27+\frac{ 11883479703715069050039355503292072191392589122471575732051571119717595548552345080072833752090814282}{ 762325578427705482137746574067229488156369299800529597635468373844463859062368874404292289563613477}I$	$0$	$0$
$27-\frac{ 11883479703715069050039355503292072191392589122471575732051571119717595548552345080072833752090814282}{ 762325578427705482137746574067229488156369299800529597635468373844463859062368874404292289563613477}I$	$0$	$0$	$0$

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3

New Number: 5.103 | AESZ: 354 | Superseeker: 25 17175 | Hash: 0d4263e8c85dceb5c51f8614f7c1bc79

Degree: 5

$\theta^4-5 x\left(170\theta^4+160\theta^3+125\theta^2+45\theta+6\right)+3 5^{3} x^{2}\left(725\theta^4+1220\theta^3+1105\theta^2+460\theta+68\right)-3^{2} 5^{5} x^{3}\left(1421\theta^4+3186\theta^3+3053\theta^2+1272\theta+188\right)+2^{2} 3^{3} 5^{7} x^{4}(3\theta+1)(3\theta+2)(34\theta^2+61\theta+36)-2^{2} 3^{4} 5^{9} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 30, 3150, 462000, 78828750, ...
--> OEIS
Normalized instanton numbers (n₀=1): 25, 2175/4, 17175, 351250, 23000351/5, ... ; Common denominator:...

Discriminant

$-(2278125z^3-84375z^2+550z-1)(-1+150z)^2$

Local exponents

$0$ ≈$0.003863-0.000232I$ ≈$0.003863+0.000232I$ $\frac{ 1}{ 150}$ ≈$0.029311$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 3}$
$0$ $1$ $1$ $1$ $1$ $\frac{ 2}{ 3}$
$0$ $1$ $1$ $3$ $1$ $\frac{ 4}{ 3}$
$0$ $2$ $2$ $4$ $2$ $\frac{ 5}{ 3}$

\(0\)	≈\(0.003863-0.000232I\)	≈\(0.003863+0.000232I\)	\(\frac{ 1}{ 150}\)	≈\(0.029311\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 3}\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(\frac{ 2}{ 3}\)
\(0\)	\(1\)	\(1\)	\(3\)	\(1\)	\(\frac{ 4}{ 3}\)
\(0\)	\(2\)	\(2\)	\(4\)	\(2\)	\(\frac{ 5}{ 3}\)

Note:

This is operator "5.103" from ...

4

New Number: 5.106 | AESZ: 360 | Superseeker: 3169/17 16293835/17 | Hash: 502b9ea354d34405e6925ab32d7f1cd2

Degree: 5

$17^{2} \theta^4+17 x\left(10622\theta^4-19904\theta^3-13913\theta^2-3961\theta-510\right)+3^{2} x^{2}\left(1596891\theta^4-10821444\theta^3+10580847\theta^2+6358884\theta+1355036\right)-3^{5} x^{3}\left(5472387\theta^4-81131922\theta^3-52565469\theta^2-9898488\theta+1434596\right)+2^{2} 3^{8} 127 x^{4}\left(318018\theta^4+157911\theta^3-445563\theta^2-476706\theta-130792\right)-2^{2} 3^{12} 5 127^{2} x^{5}(5\theta+3)(5\theta+4)(5\theta+6)(5\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 30, 414, -73680, -4205250, ...
--> OEIS
Normalized instanton numbers (n₀=1): 3169/17, -723497/68, 16293835/17, -1870341966/17, 251152956621/17, ... ; Common denominator:...

Discriminant

$-(2278125z^3-33831z^2+182z-1)(17+6858z)^2$

Local exponents

$-\frac{ 17}{ 6858}$ $0$ ≈$0.001817-0.005986I$ ≈$0.001817+0.005986I$ ≈$0.011217$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 3}{ 5}$
$1$ $0$ $1$ $1$ $1$ $\frac{ 4}{ 5}$
$3$ $0$ $1$ $1$ $1$ $\frac{ 6}{ 5}$
$4$ $0$ $2$ $2$ $2$ $\frac{ 7}{ 5}$

\(-\frac{ 17}{ 6858}\)	\(0\)	≈\(0.001817-0.005986I\)	≈\(0.001817+0.005986I\)	≈\(0.011217\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 3}{ 5}\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 4}{ 5}\)
\(3\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 6}{ 5}\)
\(4\)	\(0\)	\(2\)	\(2\)	\(2\)	\(\frac{ 7}{ 5}\)

Note:

This is operator "5.106" from ...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(880\)	\(20\)	\(68\)	\(13\)

5

New Number: 5.119 | AESZ: | Superseeker: 138 278872 | Hash: 61d7a82df3cf3c429b6286bc39ccb426

Degree: 5

$\theta^4-2 3 x\left(42\theta^4+204\theta^3+145\theta^2+43\theta+5\right)-2^{2} x^{2}\left(26932\theta^4+40768\theta^3-6943\theta^2-8482\theta-1635\right)-2^{4} 3^{2} 5 x^{3}\left(11156\theta^4+3848\theta^3+1777\theta^2+901\theta+180\right)-2^{7} 3^{3} 5^{2} x^{4}(2\theta+1)(304\theta^3+356\theta^2+97\theta-15)+2^{10} 3^{3} 5^{5} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 30, 4530, 1074900, 312527250, ...
--> OEIS
Normalized instanton numbers (n₀=1): 138, 1139, 278872, 21493934, 3832908140, ... ; Common denominator:...

Discriminant

$(4z-1)(500z-1)(12z+1)(1+120z)^2$

Local exponents

$-\frac{ 1}{ 12}$ $-\frac{ 1}{ 120}$ $0$ $\frac{ 1}{ 500}$ $\frac{ 1}{ 4}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $0$ $1$ $1$ $1$
$1$ $3$ $0$ $1$ $1$ $1$
$2$ $4$ $0$ $2$ $2$ $\frac{ 3}{ 2}$

\(-\frac{ 1}{ 12}\)	\(-\frac{ 1}{ 120}\)	\(0\)	\(\frac{ 1}{ 500}\)	\(\frac{ 1}{ 4}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)
\(1\)	\(3\)	\(0\)	\(1\)	\(1\)	\(1\)
\(2\)	\(4\)	\(0\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.119" from ...

6

New Number: 5.126 | AESZ: | Superseeker: 110 729096 | Hash: 511069e41e6328e47a1ea996049096b4

Degree: 5

$\theta^4-x\left(881\theta^4+1222\theta^3+878\theta^2+267\theta+30\right)+3 x^{2}\left(50601\theta^4+60024\theta^3+17189\theta^2+280\theta-340\right)-3^{2} 5 x^{3}\left(195867\theta^4+207846\theta^3+142719\theta^2+49068\theta+6316\right)+2^{2} 3^{4} 5^{2} x^{4}(3\theta+1)(3\theta+2)(1902\theta^2+1767\theta+386)+2^{2} 3^{6} 5^{4} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 30, 6210, 2004240, 789638850, ...
--> OEIS
Normalized instanton numbers (n₀=1): 110, 12935/2, 729096, 247828991/2, 26419290920, ... ; Common denominator:...

Discriminant

$(675z-1)(27z-1)(z+1)(-1+90z)^2$

Local exponents

$-1$ $0$ $\frac{ 1}{ 675}$ $\frac{ 1}{ 90}$ $\frac{ 1}{ 27}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 3}$
$1$ $0$ $1$ $1$ $1$ $\frac{ 2}{ 3}$
$1$ $0$ $1$ $3$ $1$ $\frac{ 4}{ 3}$
$2$ $0$ $2$ $4$ $2$ $\frac{ 5}{ 3}$

\(-1\)	\(0\)	\(\frac{ 1}{ 675}\)	\(\frac{ 1}{ 90}\)	\(\frac{ 1}{ 27}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 3}\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 2}{ 3}\)
\(1\)	\(0\)	\(1\)	\(3\)	\(1\)	\(\frac{ 4}{ 3}\)
\(2\)	\(0\)	\(2\)	\(4\)	\(2\)	\(\frac{ 5}{ 3}\)

Note:

Operator London 18.
B-Incarnation: Laurent-polynomial.

7

New Number: 5.127 | AESZ: | Superseeker: 957/10 1581774/5 | Hash: 8b1c933faa73767af598d82d1e214624

Degree: 5

$2^{2} 5^{2} \theta^4-2 3 5 x\left(1812\theta^4+3858\theta^3+2799\theta^2+870\theta+100\right)-3 x^{2}\left(293697\theta^4-124614\theta^3-930203\theta^2-562390\theta-95700\right)+3^{3} x^{3}\left(62631\theta^4+977400\theta^3+677140\theta^2+104550\theta-6300\right)+3^{5} 5 13 x^{4}(3\theta+1)(3\theta+2)(308\theta^2-16\theta-231)-3^{8} 13^{2} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 30, 5130, 1369200, 446603850, ...
--> OEIS
Normalized instanton numbers (n₀=1): 957/10, 32493/10, 1581774/5, 423123141/10, 14142369903/2, ... ; Common denominator:...

Discriminant

$-(6561z^3-4320z^2+567z-1)(10+117z)^2$

Local exponents

$-\frac{ 10}{ 117}$ $0$ ≈$0.001788$ ≈$0.178154$ ≈$0.478494$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 3}$
$1$ $0$ $1$ $1$ $1$ $\frac{ 2}{ 3}$
$3$ $0$ $1$ $1$ $1$ $\frac{ 4}{ 3}$
$4$ $0$ $2$ $2$ $2$ $\frac{ 5}{ 3}$

\(-\frac{ 10}{ 117}\)	\(0\)	≈\(0.001788\)	≈\(0.178154\)	≈\(0.478494\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 3}\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 2}{ 3}\)
\(3\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 4}{ 3}\)
\(4\)	\(0\)	\(2\)	\(2\)	\(2\)	\(\frac{ 5}{ 3}\)

Note:

Operator London 9.
B-Incarnation as Laurent-polynomial.

8

New Number: 5.81 | AESZ: 312 | Superseeker: 5/7 48/7 | Hash: 767262575f8b1458839c1e9a8beacf0a

Degree: 5

$7^{2} \theta^4-7 x\left(39\theta^4+234\theta^3+201\theta^2+84\theta+14\right)-2 x^{2}\left(12073\theta^4+43222\theta^3+57461\theta^2+34328\theta+7756\right)-2^{2} x^{3}\left(28923\theta^4+48426\theta^3-33393\theta^2-80976\theta-32032\right)+2^{3} 13 x^{4}\left(359\theta^4+9790\theta^3+20805\theta^2+15784\theta+4124\right)+2^{5} 3 13^{2} x^{5}(\theta+1)^2(6\theta+5)(6\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 2, 30, 308, 5950, ...
--> OEIS
Normalized instanton numbers (n₀=1): 5/7, 239/28, 48/7, 4451/14, 5888/7, ... ; Common denominator:...

Discriminant

$(16z+1)(2z-1)(27z-1)(7+26z)^2$

Local exponents

$-\frac{ 7}{ 26}$ $-\frac{ 1}{ 16}$ $0$ $\frac{ 1}{ 27}$ $\frac{ 1}{ 2}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 5}{ 6}$
$1$ $1$ $0$ $1$ $1$ $1$
$3$ $1$ $0$ $1$ $1$ $1$
$4$ $2$ $0$ $2$ $2$ $\frac{ 7}{ 6}$

\(-\frac{ 7}{ 26}\)	\(-\frac{ 1}{ 16}\)	\(0\)	\(\frac{ 1}{ 27}\)	\(\frac{ 1}{ 2}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 5}{ 6}\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)
\(3\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)
\(4\)	\(2\)	\(0\)	\(2\)	\(2\)	\(\frac{ 7}{ 6}\)

Note:

This is operator "5.81" from ...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-108\)	\(108\)	\(84\)	\(23\)

9

New Number: 8.63 | AESZ: | Superseeker: 8/5 67 | Hash: 2c5f91dca73abc39f5d6eb00b9c4ea16

Degree: 8

$5^{2} \theta^4-5 x\left(199\theta^4+206\theta^3+168\theta^2+65\theta+10\right)+x^{2}\left(3919\theta^4-12068\theta^3-29761\theta^2-21850\theta-5520\right)+2^{3} x^{3}\left(7540\theta^4+22092\theta^3+14577\theta^2+945\theta-1380\right)-2^{4} x^{4}\left(19051\theta^4+64358\theta^3+193446\theta^2+204083\theta+70234\right)+2^{6} x^{5}\left(9185\theta^4+171038\theta^3+422584\theta^2+391123\theta+124848\right)-2^{6} 3^{2} x^{6}\left(4673\theta^4+16800\theta^3+53963\theta^2+64704\theta+24596\right)-2^{9} 3^{4} x^{7}\left(578\theta^4+2884\theta^3+4825\theta^2+3383\theta+858\right)-2^{12} 3^{8} x^{8}\left((\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 2, 30, 488, 9934, ...
--> OEIS
Normalized instanton numbers (n₀=1): 8/5, 101/10, 67, 6197/10, 32978/5, ... ; Common denominator:...

Discriminant

$-(8z+1)(648z^3-79z^2+35z-1)(-5+32z+72z^2)^2$

Local exponents

$-\frac{ 2}{ 9}-\frac{ 1}{ 36}\sqrt{ 154}$ $-\frac{ 1}{ 8}$ $0$ ≈$0.030113$ ≈$0.0459-0.221678I$ ≈$0.0459+0.221678I$ $-\frac{ 2}{ 9}+\frac{ 1}{ 36}\sqrt{ 154}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $1$
$1$ $1$ $0$ $1$ $1$ $1$ $1$ $1$
$3$ $1$ $0$ $1$ $1$ $1$ $3$ $1$
$4$ $2$ $0$ $2$ $2$ $2$ $4$ $1$

\(-\frac{ 2}{ 9}-\frac{ 1}{ 36}\sqrt{ 154}\)	\(-\frac{ 1}{ 8}\)	\(0\)	≈\(0.030113\)	≈\(0.0459-0.221678I\)	≈\(0.0459+0.221678I\)	\(-\frac{ 2}{ 9}+\frac{ 1}{ 36}\sqrt{ 154}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(3\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(3\)	\(1\)
\(4\)	\(2\)	\(0\)	\(2\)	\(2\)	\(2\)	\(4\)	\(1\)

Note:

This is operator "8.63" from ...

\(1.052168056+.90357723e-1I\)	\(\frac{ 1}{ 4}-\frac{ 1}{ 12}I\sqrt{ 3}\)	\(-33^{ \frac{ 1}{ 6}}Pi^{ \frac{ 9}{ 2}}Zeta(5)^6-6\lambda\)	\(.10688274e-1-\frac{ 1}{ 5}I5^{ \frac{ 4}{ 7}}ln(2)^12\)
\(\frac{ 3}{ 2}-\frac{ 1}{ 2}I\sqrt{ 3}\)	\(\frac{ 3}{ 4}-\frac{ 1}{ 4}I\sqrt{ 3}\)	\(-\frac{ 1}{ 8}+\frac{ 1}{ 24}I\sqrt{ 3}\)	\(33^{ \frac{ 1}{ 6}}Pi^{ \frac{ 9}{ 2}}Zeta(5)^6+6\lambda\)
\(0\)	\(\frac{ 9}{ 2}-\frac{ 3}{ 2}I\sqrt{ 3}\)	\(\frac{ 3}{ 4}-\frac{ 1}{ 4}I\sqrt{ 3}\)	\(\frac{ 1}{ 4}-\frac{ 1}{ 12}I\sqrt{ 3}\)
\(-27+9I\sqrt{ 3}\)	\(0\)	\(\frac{ 3}{ 2}-\frac{ 1}{ 2}I\sqrt{ 3}\)	\(.447831944-.956383127I\)

\(\frac{ 1}{ 2}+36\lambda\)	\(\frac{ 1}{ 4}+6\lambda\)	\(0\)	\(.19987912e-1\)
\(0\)	\(1\)	\(0\)	\(0\)
\(-6\)	\(3\)	\(1\)	\(\frac{ 1}{ 4}-6\lambda\)
\(-36\)	\(-6\)	\(0\)	\(\frac{ 1}{ 2}-36\lambda\)

\(\frac{ 1}{ 2}-36\lambda\)	\(-3\)	\(\frac{ 5}{ 6}\)	\(1\)
\(0\)	\(12\)	\(-1\)	\(0\)
\(6\)	\(-36\)	\(0\)	\(0\)
\(36\)	\(0\)	\(0\)	\(0\)

\(-\frac{ 6521007}{ 125000000}-\frac{ 90357723}{ 1000000000}I\)	\(-3+\frac{ 4511615154067544842086723740124334848694351954431101272196462779644508392806538050844596873167533211}{ 2604782223680891931509451724762066519358428478691519147090699072692122550847025398588836869330367971}I\)	\(\frac{ 1}{ 2}-\frac{ 3081490456277555159153769728602633601692409347626414678367139999430219011336903561652776870289659281}{ 3558198688874218386798087732443200684026390216561310209643580926168315471826781724716716871248950591}I\)	\(1\)
\(-\frac{ 3}{ 2}+\frac{ 1}{ 2}I\sqrt{ 3}\)	\(\frac{ 27}{ 2}-\frac{ 5941739851857534525019677751646036095696294561235787866025785559858797774276172540036416876045407141}{ 762325578427705482137746574067229488156369299800529597635468373844463859062368874404292289563613477}I\)	\(-\frac{ 1}{ 2}+\frac{ 3081490456277555159153769728602633601692409347626414678367139999430219011336903561652776870289659281}{ 3558198688874218386798087732443200684026390216561310209643580926168315471826781724716716871248950591}I\)	\(0\)
\(0\)	\(-27+\frac{ 11883479703715069050039355503292072191392589122471575732051571119717595548552345080072833752090814282}{ 762325578427705482137746574067229488156369299800529597635468373844463859062368874404292289563613477}I\)	\(0\)	\(0\)
\(27-\frac{ 11883479703715069050039355503292072191392589122471575732051571119717595548552345080072833752090814282}{ 762325578427705482137746574067229488156369299800529597635468373844463859062368874404292289563613477}I\)	\(0\)	\(0\)	\(0\)

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:

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:

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