Calabi-Yau differential operator database v.3.0

1

New Number: 2.11 | AESZ: 69 | Superseeker: 64 246848 | Hash: 729adc350de26d9415643078ed8d3867

Degree: 2

$\theta^4-2^{2} x(4\theta+1)(4\theta+3)(10\theta^2+10\theta+3)+2^{4} 3^{2} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 36, 6300, 1718640, 575675100, ...
--> OEIS
Normalized instanton numbers (n₀=1): 64, 2616, 246848, 32024824, 5160268864, ... ; Common denominator:...

Discriminant

$(576z-1)(64z-1)$

Local exponents

$0$ $\frac{ 1}{ 576}$ $\frac{ 1}{ 64}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$0$ $1$ $1$ $\frac{ 3}{ 4}$
$0$ $1$ $1$ $\frac{ 5}{ 4}$
$0$ $2$ $2$ $\frac{ 7}{ 4}$

\(0\)	\(\frac{ 1}{ 576}\)	\(\frac{ 1}{ 64}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 3}{ 4}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 5}{ 4}\)
\(0\)	\(2\)	\(2\)	\(\frac{ 7}{ 4}\)

Note:

Hadamard product $C\ast c$

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-224\)	\(72\)	\(12\)	\(8\)

2

New Number: 2.27 | AESZ: 140 | Superseeker: 108 -4945756 | Hash: 74692097f8183c067c2c4b1a5c93387b

Degree: 2

$\theta^4-2^{2} 3 x(6\theta+1)(6\theta+5)(17\theta^2+17\theta+6)+2^{7} 3^{4} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 360, 582120, 1274232960, 3204505984680, ...
--> OEIS
Normalized instanton numbers (n₀=1): 108, 54135, -4945756, 7925523138, -2434666062240, ... ; Common denominator:...

Discriminant

$(3888z-1)(3456z-1)$

Local exponents

$0$ $\frac{ 1}{ 3888}$ $\frac{ 1}{ 3456}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 6}$
$0$ $1$ $1$ $\frac{ 5}{ 6}$
$0$ $1$ $1$ $\frac{ 7}{ 6}$
$0$ $2$ $2$ $\frac{ 11}{ 6}$

\(0\)	\(\frac{ 1}{ 3888}\)	\(\frac{ 1}{ 3456}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 6}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 5}{ 6}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 7}{ 6}\)
\(0\)	\(2\)	\(2\)	\(\frac{ 11}{ 6}\)

Note:

Hadamard product $D \ast g$

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-676\)	\(132\)	\(12\)	\(13\)

3

New Number: 2.3 | AESZ: 68 | Superseeker: 52 220220 | Hash: 13a48045ff0a42a9fcfbdb710baf1997

Degree: 2

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 24, 4200, 1034880, 311711400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 52, 2814, 220220, 29135058, 4512922272, ... ; Common denominator:...

Discriminant

$-(64z+1)(512z-1)$

Local exponents

$-\frac{ 1}{ 64}$ $0$ $\frac{ 1}{ 512}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$1$ $0$ $1$ $\frac{ 3}{ 4}$
$1$ $0$ $1$ $\frac{ 5}{ 4}$
$2$ $0$ $2$ $\frac{ 7}{ 4}$

\(-\frac{ 1}{ 64}\)	\(0\)	\(\frac{ 1}{ 512}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 3}{ 4}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 5}{ 4}\)
\(2\)	\(0\)	\(2\)	\(\frac{ 7}{ 4}\)

Note:

C*a

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-228\)	\(72\)	\(12\)	\(8\)

4

New Number: 3.17 | AESZ: 387 | Superseeker: 68 125636/3 | Hash: 06864aab02693f4b84eb494138bb3428

Degree: 3

$\theta^4-2^{2} x\left(228\theta^4+456\theta^3+385\theta^2+157\theta+26\right)+2^{11} x^{2}(\theta+1)^2(132\theta^2+264\theta+109)-2^{18} 5^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 104, 18600, 3925760, 906368680, ...
--> OEIS
Normalized instanton numbers (n₀=1): 68, 204, 125636/3, 841384, 123715360, ... ; Common denominator:...

Discriminant

$-(400z-1)(-1+256z)^2$

Local exponents

$0$ $\frac{ 1}{ 400}$ $\frac{ 1}{ 256}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $0$ $1$
$0$ $1$ $1$ $2$
$0$ $2$ $1$ $\frac{ 5}{ 2}$

\(0\)	\(\frac{ 1}{ 400}\)	\(\frac{ 1}{ 256}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(0\)	\(1\)
\(0\)	\(1\)	\(1\)	\(2\)
\(0\)	\(2\)	\(1\)	\(\frac{ 5}{ 2}\)

Note:

This is operator "3.17" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(80\)	\(24\)	\(12\)	\(4\)

5

New Number: 3.21 | AESZ: 391 | Superseeker: 964 85888580/3 | Hash: 907f1fbd0b6f7c89689fb136ee18482a

Degree: 3

$\theta^4-2^{2} x\left(3460\theta^4+5768\theta^3+4385\theta^2+1501\theta+186\right)+2^{10} 3^{2} x^{2}(4\theta+3)(1732\theta^3+4475\theta^2+3531\theta+645)-2^{14} 3^{4} 17^{2} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 744, 1731240, 5192436480, 17479541356200, ...
--> OEIS
Normalized instanton numbers (n₀=1): 964, -111140, 85888580/3, -9197858184, 3544241969952, ... ; Common denominator:...

Discriminant

$-(4624z-1)(-1+4608z)^2$

Local exponents

$0$ $\frac{ 1}{ 4624}$ $\frac{ 1}{ 4608}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$0$ $1$ $\frac{ 1}{ 2}$ $\frac{ 3}{ 4}$
$0$ $1$ $1$ $\frac{ 7}{ 4}$
$0$ $2$ $\frac{ 3}{ 2}$ $\frac{ 9}{ 4}$

\(0\)	\(\frac{ 1}{ 4624}\)	\(\frac{ 1}{ 4608}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(0\)	\(1\)	\(\frac{ 1}{ 2}\)	\(\frac{ 3}{ 4}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 7}{ 4}\)
\(0\)	\(2\)	\(\frac{ 3}{ 2}\)	\(\frac{ 9}{ 4}\)

Note:

This is operator "3.21" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(304\)	\(24\)	\(12\)	\(4\)

6

New Number: 4.33 | AESZ: 55 | Superseeker: 76/3 144196/3 | Hash: 7e88cd5b7dc1c51022b66ac6f009218f

Degree: 4

$3^{2} \theta^4-2^{2} 3 x\left(208\theta^4+224\theta^3+163\theta^2+51\theta+6\right)+2^{9} x^{2}\left(32\theta^4-928\theta^3-1606\theta^2-837\theta-141\right)+2^{16} x^{3}\left(144\theta^4+576\theta^3+467\theta^2+144\theta+15\right)-2^{24} x^{4}\left((2\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 936, 108800, 16748200, ...
--> OEIS
Normalized instanton numbers (n₀=1): 76/3, 3476/3, 144196/3, 3563196, 309069600, ... ; Common denominator:...

Discriminant

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

Local exponents

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

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

Note:

Sporadic operator. There is a second MUM-point
hiding at infinity, corresponding to Operator 4.56

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-88\)	\(48\)	\(12\)	\(6\)

7

New Number: 5.32 | AESZ: 215 | Superseeker: 220/3 89212 | Hash: ced61f5675491a3c4446c0e55e7bc36b

Degree: 5

$3^{2} \theta^4-2^{2} 3 x\left(268\theta^4+632\theta^3+463\theta^2+147\theta+18\right)-2^{7} x^{2}\left(448\theta^4-1616\theta^3-4280\theta^2-2418\theta-441\right)+2^{12} x^{3}\left(416\theta^4+2016\theta^3+756\theta^2-288\theta-135\right)+2^{19} x^{4}(8\theta^2-28\theta-33)(2\theta+1)^2-2^{24} x^{5}(2\theta+1)^2(2\theta+3)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 24, 2664, 470400, 102047400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 220/3, 3538/3, 89212, 7484350, 2459418080/3, ... ; Common denominator:...

Discriminant

$-(16z-1)(4096z^2-384z+1)(3+64z)^2$

Local exponents

$-\frac{ 3}{ 64}$ $0$ $\frac{ 3}{ 64}-\frac{ 1}{ 32}\sqrt{ 2}$ $\frac{ 1}{ 16}$ $\frac{ 3}{ 64}+\frac{ 1}{ 32}\sqrt{ 2}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $1$ $1$ $\frac{ 1}{ 2}$
$3$ $0$ $1$ $1$ $1$ $\frac{ 3}{ 2}$
$4$ $0$ $2$ $2$ $2$ $\frac{ 3}{ 2}$

\(-\frac{ 3}{ 64}\)	\(0\)	\(\frac{ 3}{ 64}-\frac{ 1}{ 32}\sqrt{ 2}\)	\(\frac{ 1}{ 16}\)	\(\frac{ 3}{ 64}+\frac{ 1}{ 32}\sqrt{ 2}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)
\(3\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 3}{ 2}\)
\(4\)	\(0\)	\(2\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.32" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-60\)	\(48\)	\(12\)	\(6\)

8

New Number: 1.5 | AESZ: 5 | Superseeker: 60 134292 | Hash: a6c4fb927cb2a4bb1103c1c739a252b0

Degree: 1

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 24, 3240, 672000, 169785000, ...
--> OEIS
Normalized instanton numbers (n₀=1): 60, 1869, 134292, 14016600, 1806410976, ... ; Common denominator:...

Discriminant

$1-432z$

Local exponents

$0$ $\frac{ 1}{ 432}$ $\infty$
$0$ $0$ $\frac{ 1}{ 3}$
$0$ $1$ $\frac{ 1}{ 2}$
$0$ $1$ $\frac{ 1}{ 2}$
$0$ $2$ $\frac{ 2}{ 3}$

\(0\)	\(\frac{ 1}{ 432}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 1}{ 3}\)
\(0\)	\(1\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(\frac{ 1}{ 2}\)
\(0\)	\(2\)	\(\frac{ 2}{ 3}\)

Note:

A-incarnation: X(2,2,3) in $P^6$.

\(4.+3.256527087I\)	\(-1-224\lambda\)	\(\frac{ 3}{ 4}+168\lambda\)	\(.44582463e-1-112\lambda\)
\(9\)	\(-2\)	\(\frac{ 9}{ 4}\)	\(-\frac{ 3}{ 4}-168\lambda\)
\(12\)	\(-4\)	\(4\)	\(-1-224\lambda\)
\(36\)	\(-12\)	\(9\)	\(-2.-3.256527087I\)

\(-5.088262696-2.403669772I\)	\(-9.231233148+8.267057761I\)	\(6.171205313+7.544982974I\)	\(3.227450678-3.068539845I\)
\(-6.270037138+8.225054977I\)	\(9.605336680+17.587574161I\)	\(14.123297626-6.142790642I\)	\(-3.279565479-6.225556868I\)
\(-2.195545276+2.457029703I\)	\(2.297135143+5.799775915I\)	\(5.638341607-1.600871223I\)	\(-.887292619-2.058764958I\)
\(-13.680081028+17.945574495I\)	\(18.775280028+38.372889078I\)	\(30.814467548-13.402452309I\)	\(-6.155415591-13.583033166I\)

\(4.+2.209786237I\)	\(-1.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-1.104893119I\)	\(1+152\lambda\)	\(-.171535199-114\lambda\)
\(8\)	\(-3\)	\(\frac{ 8}{ 3}\)	\(-1-152\lambda\)
\(12\)	\(-6\)	\(5\)	\(-1.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-1.104893119I\)
\(24\)	\(-12\)	\(8\)	\(-2.-2.209786237I\)

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

\(1+224\lambda\)	\(0\)	\(56\lambda\)	\(.98194154e-1\)
\(3\)	\(1\)	\(\frac{ 3}{ 4}\)	\(-56\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(12\)	\(0\)	\(3\)	\(1-224\lambda\)

\(-224\lambda\)	\(5\)	\(1\)	\(1\)
\(-3\)	\(-6\)	\(-1\)	\(0\)
\(0\)	\(12\)	\(0\)	\(0\)
\(-12\)	\(0\)	\(0\)	\(0\)

\(1.+3.275911176I\)	\(0\)	\(1.501459289I\)	\(.894299503\)
\(\frac{ 11}{ 2}\)	\(1\)	\(\frac{ 121}{ 48}\)	\(-1.501459289I\)
\(0\)	\(0\)	\(1\)	\(0\)
\(12\)	\(0\)	\(\frac{ 11}{ 2}\)	\(1.-3.275911176I\)

\(-\frac{ 409488897}{ 125000000}I\)	\(\frac{ 15}{ 2}\)	\(1\)	\(1\)
\(-\frac{ 11}{ 2}\)	\(-6\)	\(-1\)	\(0\)
\(0\)	\(12\)	\(0\)	\(0\)
\(-12\)	\(0\)	\(0\)	\(0\)

\(1.+1.104893119I\)	\(0\)	\(57\lambda\)	\(\frac{ 276}{ 2713}\)
\(3\)	\(1\)	\(\frac{ 3}{ 4}\)	\(-57\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(12\)	\(0\)	\(3\)	\(1.-1.104893119I\)

\(-\frac{ 1104893119}{ 1000000000}I\)	\(5\)	\(1\)	\(1\)
\(-3\)	\(-6\)	\(-1\)	\(0\)
\(0\)	\(12\)	\(0\)	\(0\)
\(-12\)	\(0\)	\(0\)	\(0\)

\(80\lambda\)	\(3\)	\(1\)	\(1\)
\(-1\)	\(-6\)	\(-1\)	\(0\)
\(0\)	\(12\)	\(0\)	\(0\)
\(-12\)	\(0\)	\(0\)	\(0\)

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:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Explicit solution

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:

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