Calabi-Yau differential operator database v.3.0

Summary

You searched for: c3=192

Your search produced 2 matches

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New Number: 4.64 | AESZ: 295 | Superseeker: -5408 -4296119968 | Hash: e40629f953a095a2a764c68394321139

Degree: 4

$\theta^4-2^{4} x\left(816\theta^4-1440\theta^3-904\theta^2-184\theta-17\right)+2^{18} x^{2}\left(80\theta^4-592\theta^3+432\theta^2+164\theta+23\right)+2^{30} x^{3}\left(80\theta^4-384\theta^3-296\theta^2-96\theta-11\right)+2^{45} x^{4}\left((2\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, -272, 93456, 194502400, -587215823600, ...
--> OEIS
Normalized instanton numbers (n₀=1): -5408, -3839480, -4296119968, -6482749129792, -11816577914904160, ... ; Common denominator:...

Discriminant

$(8388608z^2+3328z+1)(-1+8192z)^2$

Local exponents

$-\frac{ 13}{ 65536}-\frac{ 7}{ 65536}\sqrt{ 7}I$ $-\frac{ 13}{ 65536}+\frac{ 7}{ 65536}\sqrt{ 7}I$ $0$ $s_1$ $s_2$ $\frac{ 1}{ 8192}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $0$ $1$ $1$ $1$ $\frac{ 1}{ 2}$
$1$ $1$ $0$ $1$ $1$ $3$ $\frac{ 1}{ 2}$
$2$ $2$ $0$ $2$ $2$ $4$ $\frac{ 1}{ 2}$

\(-\frac{ 13}{ 65536}-\frac{ 7}{ 65536}\sqrt{ 7}I\)	\(-\frac{ 13}{ 65536}+\frac{ 7}{ 65536}\sqrt{ 7}I\)	\(0\)	\(s_1\)	\(s_2\)	\(\frac{ 1}{ 8192}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(3\)	\(\frac{ 1}{ 2}\)
\(2\)	\(2\)	\(0\)	\(2\)	\(2\)	\(4\)	\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at
infinity, corresponding to Operator AESZ 296/4.65

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(192\)	\(4\)	\(4\)	\(1\)

New Number: 8.5 | AESZ: 173 | Superseeker: 11 -2434/3 | Hash: afa82ed9ee239bb5fcac960f8884db01

Degree: 8

$\theta^4-x(7\theta^2+7\theta+2)(17\theta^2+17\theta+6)+2^{6} x^{2}\left(55\theta^4+112\theta^3+155\theta^2+86\theta+15\right)-2^{6} 3^{2} x^{3}\left(119\theta^4-714\theta^3-2185\theta^2-1656\theta-444\right)+2^{12} 3^{2} x^{4}\left(92\theta^4+184\theta^3+98\theta^2+6\theta+9\right)+2^{12} 3^{4} x^{5}\left(119\theta^4+1190\theta^3+671\theta^2-96\theta-140\right)+2^{18} 3^{4} x^{6}\left(55\theta^4+108\theta^3+149\theta^2+108\theta+27\right)+2^{18} 3^{6} x^{7}(7\theta^2+7\theta+2)(17\theta^2+17\theta+6)+2^{24} 3^{8} x^{8}\left((\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 12, 420, 17472, 828324, ...
--> OEIS
Normalized instanton numbers (n₀=1): 11, 229/4, -2434/3, 7512, 54801, ... ; Common denominator:...

Discriminant

$(72z-1)(8z+1)(64z-1)(9z+1)(1+576z^2)^2$

Local exponents

$-\frac{ 1}{ 8}$ $-\frac{ 1}{ 9}$ $0-\frac{ 1}{ 24}I$ $0$ $0+\frac{ 1}{ 24}I$ $\frac{ 1}{ 72}$ $\frac{ 1}{ 64}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $0$ $1$
$1$ $1$ $1$ $0$ $1$ $1$ $1$ $1$
$1$ $1$ $3$ $0$ $3$ $1$ $1$ $1$
$2$ $2$ $4$ $0$ $4$ $2$ $2$ $1$

\(-\frac{ 1}{ 8}\)	\(-\frac{ 1}{ 9}\)	\(0-\frac{ 1}{ 24}I\)	\(0\)	\(0+\frac{ 1}{ 24}I\)	\(\frac{ 1}{ 72}\)	\(\frac{ 1}{ 64}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(1\)
\(1\)	\(1\)	\(3\)	\(0\)	\(3\)	\(1\)	\(1\)	\(1\)
\(2\)	\(2\)	\(4\)	\(0\)	\(4\)	\(2\)	\(2\)	\(1\)

Note:

Hadamard product $a \ast g$. This operator has a second MUM-point at infinity with the same instanton numbers.
It can be reduced to an operator of degree 4 with a single MUM-point defined over
$Q(\sqrt{?})$.

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:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice