Calabi-Yau differential operator database v.3.0

Summary

You searched for: c2h=120

Your search produced 2 matches

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New Number: 2.26 | AESZ: 139 | Superseeker: 44 22500 | Hash: f5d9215987323abcff6ed8709927af5d

Degree: 2

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 72, 17640, 5765760, 2156754600, ...
--> OEIS
Normalized instanton numbers (n₀=1): 44, 607, 22500, 1444678, 128626784, ... ; Common denominator:...

Discriminant

$(576z-1)(512z-1)$

Local exponents

$0$ $\frac{ 1}{ 576}$ $\frac{ 1}{ 512}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$0$ $1$ $1$ $\frac{ 3}{ 4}$
$0$ $1$ $1$ $\frac{ 5}{ 4}$
$0$ $2$ $2$ $\frac{ 7}{ 4}$

\(0\)	\(\frac{ 1}{ 576}\)	\(\frac{ 1}{ 512}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 3}{ 4}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 5}{ 4}\)
\(0\)	\(2\)	\(2\)	\(\frac{ 7}{ 4}\)

Note:

Hadamard product $C \ast g$

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-344\)	\(120\)	\(24\)	\(14\)

New Number: 3.1 | AESZ: 34 | Superseeker: 1 28/3 | Hash: e5461c5f5ae4d929328f66b8955a31f5

Degree: 3

$\theta^4-x\left(35\theta^4+70\theta^3+63\theta^2+28\theta+5\right)+x^{2}(\theta+1)^2(259\theta^2+518\theta+285)-3^{2} 5^{2} x^{3}(\theta+1)^2(\theta+2)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 5, 45, 545, 7885, ...
--> OEIS
Normalized instanton numbers (n₀=1): 1, 2, 28/3, 52, 350, ... ; Common denominator:...

Discriminant

$-(z-1)(25z-1)(9z-1)$

Local exponents

$0$ $\frac{ 1}{ 25}$ $\frac{ 1}{ 9}$ $1$ $\infty$
$0$ $0$ $0$ $0$ $1$
$0$ $1$ $1$ $1$ $1$
$0$ $1$ $1$ $1$ $2$
$0$ $2$ $2$ $2$ $2$

\(-1.363320470+.333408287I\)	\(-2.378556075+\frac{ 1}{ 4}I2^{ \frac{ 1}{ 4}}Pi^{ \frac{ 3}{ 2}}ln(2)^(\frac{ 7}{ 4})\)	\(1.952097134+1.450430332I\)	\(.352541506-.730455452I\)
\(-2.231842169+5.463251200I\)	\(4.752377305+8.996899861I\)	\(5.529765042-2.362775601I\)	\(-1.121053097-1.662936757I\)
\(-1.857729799+3.694349576I\)	\(2.129374012+I7^{ \frac{ 7}{ 8}}ln(2)^{ \frac{ 1}{ 2}}ln(3)^(\frac{ 1}{ 6})\)	\(4.991998028-1.348211717I\)	\(-.692201690-1.222934527I\)
\(-10.712842412+26.223605760I\)	\(18.011411066+43.185119335I\)	\(26.542872203-11.341322886I\)	\(-4.381054863-7.982096432I\)

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

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

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

\(1+344\lambda\)	\(0\)	\(\frac{ 215}{ 3}\lambda\)	\(.115791449\)
\(5\)	\(1\)	\(\frac{ 25}{ 24}\)	\(-\frac{ 215}{ 3}\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(24\)	\(0\)	\(5\)	\(1-344\lambda\)

\(-344\lambda\)	\(9\)	\(1\)	\(1\)
\(-5\)	\(-12\)	\(-1\)	\(0\)
\(0\)	\(24\)	\(0\)	\(0\)
\(-24\)	\(0\)	\(0\)	\(0\)

\(-80\lambda\)	\(25\)	\(1\)	\(1\)
\(-5\)	\(-60\)	\(-1\)	\(0\)
\(0\)	\(120\)	\(0\)	\(0\)
\(-120\)	\(0\)	\(0\)	\(0\)