New Number: 2.24 | AESZ: 137 | Superseeker: 20 1684/3 | Hash: 198d6c822d6c46225ac2553d60df6539
Degree: 2
\(\theta^4-2^{2} x(2\theta+1)^2(17\theta^2+17\theta+6)+2^{7} 3^{2} x^{2}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTex Coefficients of the holomorphic solution: 1, 24, 1512, 124800, 11730600, ... --> OEIS Normalized instanton numbers (n0=1): 20, 2, 1684/3, 7602, 173472, ... ; Common denominator:...
Discriminant
\((144z-1)(128z-1)\)
Local exponents
Note:
Hadamard product $A \ast g$.
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 20, 36, 15176, 486564, 21684020, 1209684456, 58513394904,...
Coefficients of the q-coordinate : 0, 1, -68, 3294, -132944, 4754733, -156431544, 4806781970,...
| Gopakumar-Vafa invariants |
|---|
| g=0 | ,... |
| g=1 | ,... |
| g=2 | ,... |
Explicit solution
\(A_{n}=\dbinom{2n}{n}^2\sum_{j,k}^{n}(-1)^{j}8^{n-j}\dbinom{n}{j}\dbinom{j}{k}^3\)
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 | \(1+16\lambda\) | \(0\) | \(\frac{ 4}{ 3}\lambda\) | \(.125248e-3\) |
| \(4\) | \(1\) | \(\frac{ 1}{ 3}\) | \(-\frac{ 4}{ 3}\lambda\) |
| \(0\) | \(0\) | \(1\) | \(0\) |
| \(48\) | \(0\) | \(4\) | \(1-16\lambda\) |
copy data | \(.924152876+.943952044I\) | \(.188111204+1.275393351I\) | \(.593885779-.164736576I\) | \(-.98788356e-1-.111719004I\) |
| \(.205812544+3.214663066I\) | \(2.256285526+4.201440782I\) | \(1.918711704-.844672672I\) | \(-.387126151-.327818207I\) |
| \(-.81202836e-1+5.639775328I\) | \(1.617313859+7.506248400I\) | \(4.465075410-1.211574339I\) | \(-.630856884-.62528948587308939323761000463177396943029180176007410838351088466882816118573413617415470125057897174617878647522000926354793886058360352014821676702176933765632237146827234830940250115794349235757295I\) |
| \(2.469750531+38.575956789I\) | \(15.075426310+50.417289384I\) | \(23.024540442-10.136072063I\) | \(-3.645513812-3.933818487I\) |
copy data Basis of the Doran-Morgan lattice
| \(-16\lambda\) | \(12\) | \(1\) | \(1\) |
| \(-4\) | \(-24\) | \(-1\) | \(0\) |
| \(0\) | \(48\) | \(0\) | \(0\) |
| \(-48\) | \(0\) | \(0\) | \(0\) |
copy data