New Number: 2.5 | AESZ: 25 | Superseeker: 20 8220 | Hash: 93279abcbeeade30c29508de7784e582
Degree: 2
\(\theta^4-2^{2} x(2\theta+1)^2(11\theta^2+11\theta+3)-2^{4} x^{2}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTex Coefficients of the holomorphic solution: 1, 12, 684, 58800, 6129900, ... --> OEIS Normalized instanton numbers (n0=1): 20, 277, 8220, 352994, 18651536, ... ; Common denominator:...
Discriminant
\(1-176z-256z^2\)
Local exponents
Note:
Hadamard product $A\ast b$
A-incarnation: X(1,2,2) in G(2,5)
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 20, 2236, 221960, 22593852, 2331442020, 243349644568, 25610987588920,...
Coefficients of the q-coordinate : 0, 1, -44, 486, -11184, -390527, -28173000, -2131044622,...
| Gopakumar-Vafa invariants |
---|
g=0 | 400, 5540, 164400, 7059880, 373030720, 22532353740, 1493352046000, 105953648564840,... |
g=1 | 0, 0, 0, 1537, 882496, 214941640, 37001766880, 5388182343297,... |
g=2 | ,... |
Explicit solution
\(A_{n}=\dbinom{2n}{n}^2\sum_{k=0}^{n}\dbinom{n}{k}^2\dbinom{n+k}{n}\)
Maple LaTex Characteristic classes:
Monodromy (with respect to Frobenius basis)
\(\frac{ 16}{ 3}+480\lambda\) | \(-\frac{ 13}{ 6}-240\lambda\) | \(\frac{ 299}{ 360}+92\lambda\) | \(-.167088493-52\lambda\) |
\(\frac{ 46}{ 3}\) | \(-\frac{ 20}{ 3}\) | \(\frac{ 529}{ 180}\) | \(-\frac{ 299}{ 360}-92\lambda\) |
\(40\) | \(-20\) | \(\frac{ 26}{ 3}\) | \(-\frac{ 13}{ 6}-240\lambda\) |
\(80\) | \(-40\) | \(\frac{ 46}{ 3}\) | \(-\frac{ 10}{ 3}-480\lambda\) |
copy data \(1\) | \(-1\) | \(\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 6}\) |
\(0\) | \(1\) | \(-1\) | \(\frac{ 1}{ 2}\) |
\(0\) | \(0\) | \(1\) | \(-1\) |
\(0\) | \(0\) | \(0\) | \(1\) |
copy data \(1+120\lambda\) | \(0\) | \(17\lambda\) | \(.16908432e-1\) |
\(\frac{ 17}{ 6}\) | \(1\) | \(\frac{ 289}{ 720}\) | \(-17\lambda\) |
\(0\) | \(0\) | \(1\) | \(0\) |
\(20\) | \(0\) | \(\frac{ 17}{ 6}\) | \(1-120\lambda\) |
copy data Basis of the Doran-Morgan lattice
\(-120\lambda\) | \(\frac{ 37}{ 6}\) | \(1\) | \(1\) |
\(-\frac{ 17}{ 6}\) | \(-10\) | \(-1\) | \(0\) |
\(0\) | \(20\) | \(0\) | \(0\) |
\(-20\) | \(0\) | \(0\) | \(0\) |
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