New Number: 2.15 | AESZ: 38 | Superseeker: 48 73328 | Hash: 9ce26bb7405c3b98d8aeae5b1102c611
Degree: 2
\(\theta^4-2^{4} x(4\theta+1)(4\theta+3)(3\theta^2+3\theta+1)+2^{9} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)\)
Maple LaTex Coefficients of the holomorphic solution: 1, 48, 8400, 2069760, 609008400, ... --> OEIS Normalized instanton numbers (n0=1): 48, 998, 73328, 7388135, 857248528, ... ; Common denominator:...
Discriminant
\((512z-1)(256z-1)\)
Local exponents
Note:
Hadamard product $C\ast d$
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 48, 8032, 1979904, 472848672, 107156066048, 24205631604736, 5536680545574912,...
Coefficients of the q-coordinate : 0, 1, -208, 32000, -4613120, 605381040, -78889707008, 9643425928192,...
| Gopakumar-Vafa invariants |
---|
g=0 | ,... |
g=1 | ,... |
g=2 | ,... |
Explicit solution
\(A_{n}=\dbinom{2n}{n}\dbinom{4n}{2n}\sum_{k=0}^{n}\dbinom{n}{k}\dbinom{2k}{k}\dbinom{2n-2k}{n-k}\)
Maple LaTex Characteristic classes:
Monodromy (with respect to Frobenius basis)
\(1\) | \(-1\) | \(\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 6}\) |
\(0\) | \(1\) | \(-1\) | \(\frac{ 1}{ 2}\) |
\(0\) | \(0\) | \(1\) | \(-1\) |
\(0\) | \(0\) | \(0\) | \(1\) |
copy data \(1+268\lambda\) | \(0\) | \(Iarctan(\frac{ 173}{ 564})\) | \(.105419378\) |
\(\frac{ 11}{ 3}\) | \(1\) | \(\frac{ 121}{ 144}\) | \(-Iarctan(\frac{ 173}{ 564})\) |
\(0\) | \(0\) | \(1\) | \(0\) |
\(16\) | \(0\) | \(\frac{ 11}{ 3}\) | \(1-268\lambda\) |
copy data \(\frac{ 19}{ 6}+4Iln(2)^{ \frac{ 6}{ 5}}Zeta(5)^(\frac{ 2}{ 9})\) | \(-\frac{ 13}{ 24}-134\lambda\) | \(.49652777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778+.595253091I\) | \(.64137367e-1-.351740463I\) |
\(\frac{ 22}{ 3}+\frac{ 3}{ 1000000000}I\) | \(-\frac{ 5}{ 6}+\frac{ 1}{ 500000000}I\) | \(\frac{ 121}{ 72}-\frac{ 1}{ 500000000}I\) | \(-.49652777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778-.595253091I\) |
\(8+\frac{ 3}{ 1000000000}I\) | \(-2+\frac{ 1}{ 500000000}I\) | \(\frac{ 17}{ 6}-\frac{ 1}{ 500000000}I\) | \(-\frac{ 13}{ 24}-134\lambda\) |
\(32+\frac{ 7}{ 500000000}I\) | \(-8+\frac{ 7}{ 1000000000}I\) | \(\frac{ 22}{ 3}-\frac{ 7}{ 1000000000}I\) | \(-\frac{ 7}{ 6}-4Iln(2)^{ \frac{ 6}{ 5}}Zeta(5)^(\frac{ 2}{ 9})\) |
copy data Basis of the Doran-Morgan lattice
\(-268\lambda\) | \(\frac{ 19}{ 3}\) | \(1\) | \(1\) |
\(-\frac{ 11}{ 3}\) | \(-8\) | \(-1\) | \(0\) |
\(0\) | \(16\) | \(0\) | \(0\) |
\(-16\) | \(0\) | \(0\) | \(0\) |
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