Calabi-Yau differential operator database v.3.0

Summary

Your search produced exactly one match

New Number: 2.40 | AESZ: | Superseeker: -791200 -4288711075194400 | Hash: 43d26d7aa358d5634e12c133ddc42a01

Degree: 2

$\theta^4-2^{4} 5 x\left(80000\theta^4+160000\theta^3+186000\theta^2+106000\theta+22811\right)+2^{16} 5^{6} x^{2}(10\theta+7)(10\theta+9)(10\theta+11)(10\theta+13)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 1824880, 4485741488400, 12079072308276832000, 33999719248816985649610000, ...
--> OEIS
Normalized instanton numbers (n₀=1): -791200, -41486886600, -4288711075194400, -585926703697412494000, -93381074165698184340671200, ... ; Common denominator:...

Discriminant

$(3200000z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 3200000}$ $\infty$
$0$ $0$ $\frac{ 7}{ 10}$
$0$ $-\frac{ 1}{ 2}$ $\frac{ 9}{ 10}$
$0$ $1$ $\frac{ 11}{ 10}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 13}{ 10}$

\(0\)	\(\frac{ 1}{ 3200000}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 7}{ 10}\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 9}{ 10}\)
\(0\)	\(1\)	\(\frac{ 11}{ 10}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 13}{ 10}\)

Note:

Operator equivalent to $\hat{2}$ of AESZ.

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

\(cy[DM_basis]\)	\(\)	\(\)	\(\)
\(\)	\(\)	\(\)	\(\)
\(\)	\(\)	\(\)	\(\)
\(\)	\(\)	\(\)	\(\)

Calabi-Yau differential operator database v.3

Summary

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

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

\(\frac{ 35}{ 24}\)	\(-580\lambda\)	\(-\frac{ 649}{ 576}\)	\(0\)
\(0\)	\(-\frac{ 35}{ 24}\)	\(0\)	\(-\frac{ 649}{ 576}\)
\(1\)	\(0\)	\(-\frac{ 35}{ 24}\)	\(580\lambda\)
\(0\)	\(1\)	\(0\)	\(\frac{ 35}{ 24}\)