Calabi-Yau differential operator database v.3.0

Summary

You searched for: c3=-162

Your search produced 2 matches

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New Number: 2.14 | AESZ: 48 | Superseeker: 24 5832 | Hash: 8081a3989d09a7d612953dac3341d90c

Degree: 2

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 24, 1800, 188160, 23423400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 24, 291/2, 5832, 247116, 12634944, ... ; Common denominator:...

Discriminant

$(216z-1)(108z-1)$

Local exponents

$0$ $\frac{ 1}{ 216}$ $\frac{ 1}{ 108}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 3}$
$0$ $1$ $1$ $\frac{ 2}{ 3}$
$0$ $1$ $1$ $\frac{ 4}{ 3}$
$0$ $2$ $2$ $\frac{ 5}{ 3}$

\(0\)	\(\frac{ 1}{ 216}\)	\(\frac{ 1}{ 108}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 3}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 2}{ 3}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 4}{ 3}\)
\(0\)	\(2\)	\(2\)	\(\frac{ 5}{ 3}\)

Note:

B*d

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-162\)	\(84\)	\(24\)	\(11\)

New Number: 2.2 | AESZ: 15 | Superseeker: 21 15894 | Hash: c8053e0e9c05ef468263fafd5e3fc764

Degree: 2

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 12, 900, 94080, 11988900, ...
--> OEIS
Normalized instanton numbers (n₀=1): 21, 480, 15894, 894075, 58703151, ... ; Common denominator:...

Discriminant

$-(27z+1)(216z-1)$

Local exponents

$-\frac{ 1}{ 27}$ $0$ $\frac{ 1}{ 216}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 3}$
$1$ $0$ $1$ $\frac{ 2}{ 3}$
$1$ $0$ $1$ $\frac{ 4}{ 3}$
$2$ $0$ $2$ $\frac{ 5}{ 3}$

\(-\frac{ 1}{ 27}\)	\(0\)	\(\frac{ 1}{ 216}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 3}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 2}{ 3}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 4}{ 3}\)
\(2\)	\(0\)	\(2\)	\(\frac{ 5}{ 3}\)

Note:

Hadamard product $B\ast a$.

A-Incarnation: diagonal of (3,3)-intersection in $P^2 \times P^2$

\(\frac{ 13}{ 4}+324\lambda\)	\(-\frac{ 9}{ 16}-81\lambda\)	\(\frac{ 21}{ 64}+\frac{ 189}{ 4}\lambda\)	\(-.54109387e-1-\frac{ 243}{ 8}\lambda\)
\(7+\frac{ 1}{ 500000000}I\)	\(-\frac{ 3}{ 4}+\frac{ 1}{ 1000000000}I\)	\(\frac{ 49}{ 48}-\frac{ 1}{ 1000000000}I\)	\(-\frac{ 21}{ 64}-\frac{ 189}{ 4}\lambda\)
\(12+\frac{ 1}{ 250000000}I\)	\(-3+\frac{ 1}{ 500000000}I\)	\(\frac{ 11}{ 4}-\frac{ 1}{ 500000000}I\)	\(-\frac{ 9}{ 16}-81\lambda\)
\(48.+.19e-7I\)	\(-11.999999983+.80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8I\)	\(7-\frac{ 1}{ 125000000}I\)	\(-\frac{ 5}{ 4}-324\lambda\)

\(4+324\lambda\)	\(-\frac{ 3}{ 2}-162\lambda\)	\(\frac{ 3}{ 4}+81\lambda\)	\(-\frac{ 222}{ 1223}-54\lambda\)
\(9\)	\(-\frac{ 7}{ 2}\)	\(\frac{ 9}{ 4}\)	\(-\frac{ 3}{ 4}-81\lambda\)
\(18\)	\(-9\)	\(\frac{ 11}{ 2}\)	\(-\frac{ 3}{ 2}-162\lambda\)
\(36\)	\(-18\)	\(9\)	\(-2-324\lambda\)

\(1+162\lambda\)	\(0\)	\(27\lambda\)	\(.34239575e-1\)
\(3\)	\(1\)	\(\frac{ 1}{ 2}\)	\(-27\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(18\)	\(0\)	\(3\)	\(1-162\lambda\)

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:

Explicit solution

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

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

\(1+162\lambda\)	\(0\)	\(\frac{ 189}{ 8}\lambda\)	\(.25679681e-1\)
\(\frac{ 7}{ 2}\)	\(1\)	\(\frac{ 49}{ 96}\)	\(-\frac{ 189}{ 8}\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(24\)	\(0\)	\(\frac{ 7}{ 2}\)	\(1-162\lambda\)

\(-162\lambda\)	\(\frac{ 15}{ 2}\)	\(1\)	\(1\)
\(-\frac{ 7}{ 2}\)	\(-12\)	\(-1\)	\(0\)
\(0\)	\(24\)	\(0\)	\(0\)
\(-24\)	\(0\)	\(0\)	\(0\)

\(-162\lambda\)	\(6\)	\(1\)	\(1\)
\(-3\)	\(-9\)	\(-1\)	\(0\)
\(0\)	\(18\)	\(0\)	\(0\)
\(-18\)	\(0\)	\(0\)	\(0\)