New Number: 2.31 | AESZ: 7** | Superseeker: 96 -12064 | Hash: 2c494088fc85599f73fb344776dbbb28
Degree: 2
\(\theta^4-2^{4} x(2\theta+1)^2(32\theta^2+32\theta+13)+2^{16} x^{2}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTex Coefficients of the holomorphic solution: 1, 208, 107280, 70739200, 52362595600, ... --> OEIS Normalized instanton numbers (n0=1): 96, -3560, -12064, 1941800, -489007584, ... ; Common denominator:...
Discriminant
\((1024z-1)^2\)
Local exponents
Note:
This operator replaces AESZ 43, to which it is equivalent.
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 96, -28384, -325632, 124246816, -61125947904, 3358543443968, -135283661930496,...
Coefficients of the q-coordinate : 0, 1, -512, 184160, -54147072, 13983267376, -3286874001408, 718480223310336,...
| Gopakumar-Vafa invariants |
---|
g=0 | ,... |
g=1 | ,... |
g=2 | ,... |
Explicit solution
\(A_{n}=\dbinom{2n}{n}^2 64^{n}\sum_{k=0}^{n}(-1)^{k}\dbinom{-3/4}{k}\dbinom{-1/4}{n-k}^2\)
Maple LaTex No topological data
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 \(-\frac{ 1}{ 3}+Iarctan(\frac{ 244}{ 63})\) | \(\frac{ 2}{ 3}+136\lambda\) | \(\frac{ 1}{ 9}-\frac{ 68}{ 3}\lambda\) | \(.5042804e-2\) |
\(\frac{ 2}{ 3}\) | \(\frac{ 4}{ 3}\) | \(-\frac{ 1}{ 18}\) | \(\frac{ 1}{ 9}+\frac{ 68}{ 3}\lambda\) |
\(-4\) | \(2\) | \(\frac{ 4}{ 3}\) | \(\frac{ 2}{ 3}-136\lambda\) |
\(-8\) | \(-4\) | \(\frac{ 2}{ 3}\) | \(-\frac{ 1}{ 3}-Iarctan(\frac{ 244}{ 63})\) |
copy data Basis of the Doran-Morgan lattice
\(\frac{ 4}{ 3}-\frac{ 1708656527755053726527184603581775358292629291158824225586117747415508815310392346494291960809911989}{ 1296284848710416017198988117968146871699058960076991381465223285947803281706700313960088400294610326}I\) | \(\frac{ 4}{ 3}\) | \(\frac{ 1}{ 2}\) | \(1\) |
\(-\frac{ 2}{ 3}\) | \(0\) | \(-1\) | \(0\) |
\(4\) | \(-8\) | \(0\) | \(0\) |
\(8\) | \(0\) | \(0\) | \(0\) |
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