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
Note:
B*d
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 24, 1188, 157488, 15816612, 1579368024, 154234265832, 15276585787536,...
Coefficients of the q-coordinate : 0, 1, -84, 4950, -267760, 12647805, -598963032, 25047931322,...
| Gopakumar-Vafa invariants |
---|
g=0 | ,... |
g=1 | ,... |
g=2 | ,... |
Explicit solution
\(A_{n}=\dbinom{2n}{n}\dbinom{3n}{n}\sum_{k=0}^{n}\dbinom{n}{k}\dbinom{2k}{k}\dbinom{2n-2k}{n-k}\)
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 \(1+162\lambda\) | \(0\) | \(\frac{ 189}{ 8}\lambda\) | \(.25679681e-1\) |
\(\frac{ 7}{ 2}\) | \(1\) | \(\frac{ 49}{ 96}\) | \(-\frac{ 189}{ 8}\lambda\) |
\(0\) | \(0\) | \(1\) | \(0\) |
\(24\) | \(0\) | \(\frac{ 7}{ 2}\) | \(1-162\lambda\) |
copy data \(\frac{ 13}{ 4}+324\lambda\) | \(-\frac{ 9}{ 16}-81\lambda\) | \(\frac{ 21}{ 64}+\frac{ 189}{ 4}\lambda\) | \(-.54109387e-1-\frac{ 243}{ 8}\lambda\) |
\(7+\frac{ 1}{ 500000000}I\) | \(-\frac{ 3}{ 4}+\frac{ 1}{ 1000000000}I\) | \(\frac{ 49}{ 48}-\frac{ 1}{ 1000000000}I\) | \(-\frac{ 21}{ 64}-\frac{ 189}{ 4}\lambda\) |
\(12+\frac{ 1}{ 250000000}I\) | \(-3+\frac{ 1}{ 500000000}I\) | \(\frac{ 11}{ 4}-\frac{ 1}{ 500000000}I\) | \(-\frac{ 9}{ 16}-81\lambda\) |
\(48.+.19e-7I\) | \(-11.999999983+.80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8I\) | \(7-\frac{ 1}{ 125000000}I\) | \(-\frac{ 5}{ 4}-324\lambda\) |
copy data Basis of the Doran-Morgan lattice
\(-162\lambda\) | \(\frac{ 15}{ 2}\) | \(1\) | \(1\) |
\(-\frac{ 7}{ 2}\) | \(-12\) | \(-1\) | \(0\) |
\(0\) | \(24\) | \(0\) | \(0\) |
\(-24\) | \(0\) | \(0\) | \(0\) |
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