1
New Number: 3.12 | AESZ: | Superseeker: 252 1162036 | Hash: baa148eb1a5a05a0d9aca4c78be26905
Degree: 3
\(\theta^4-2^{2} 3^{2} x\left(132\theta^4+216\theta^3+165\theta^2+57\theta+7\right)+2^{4} 3^{6} x^{2}(4\theta+3)(160\theta^3+408\theta^2+316\theta+57)-2^{8} 3^{10} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 252, 202500, 212132880, 251548748100, ... --> OEIS Normalized instanton numbers (n0=1): 252, -19512, 1162036, -91851948, 24209298720, ... ; Common denominator:...
\(-(1296z-1)(-1+1728z)^2\)
| \(0\) | \(\frac{ 1}{ 1728}\) | \(\frac{ 1}{ 1296}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 4}\) |
| \(0\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 3}{ 4}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 7}{ 4}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(2\) | \(\frac{ 9}{ 4}\) |
2
New Number: 3.13 | AESZ: | Superseeker: 352 15001120/3 | Hash: b5a6f76d274395537de2c3169fdac9bf
Degree: 3
\(\theta^4-2^{2} x\left(688\theta^4+1232\theta^3+902\theta^2+286\theta+33\right)+2^{4} 3^{2} x^{2}(4\theta+3)(3776\theta^3+10096\theta^2+8268\theta+1515)-2^{10} 3^{4} 5^{2} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 132, 62748, 43686384, 37830871260, ... --> OEIS Normalized instanton numbers (n0=1): 352, 18676, 15001120/3, 1489325052, 586526654304, ... ; Common denominator:...
\(-(1600z-1)(-1+576z)^2\)
| \(0\) | \(\frac{ 1}{ 1600}\) | \(\frac{ 1}{ 576}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 4}\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 4}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 7}{ 4}\) |
| \(0\) | \(2\) | \(\frac{ 3}{ 2}\) | \(\frac{ 9}{ 4}\) |
3
New Number: 3.14 | AESZ: | Superseeker: 444 19050964 | Hash: dc96aa2da269d989ee90c49dab6a9c5a
Degree: 3
\(\theta^4-2^{2} x\left(452\theta^4+920\theta^3+633\theta^2+173\theta+17\right)-2^{4} x^{2}(4\theta+3)(3808\theta^3+10504\theta^2+8884\theta+1635)-2^{8} 11^{2} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 68, 42220, 38866320, 43812369900, ... --> OEIS Normalized instanton numbers (n0=1): 444, 57104, 19050964, 9432910668, 5781274591408, ... ; Common denominator:...
\(-(1936z-1)(1+64z)^2\)
| \(-\frac{ 1}{ 64}\) | \(0\) | \(\frac{ 1}{ 1936}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 4}\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(0\) | \(1\) | \(\frac{ 7}{ 4}\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(2\) | \(\frac{ 9}{ 4}\) |
4
New Number: 3.21 | AESZ: 391 | Superseeker: 964 85888580/3 | Hash: 907f1fbd0b6f7c89689fb136ee18482a
Degree: 3
\(\theta^4-2^{2} x\left(3460\theta^4+5768\theta^3+4385\theta^2+1501\theta+186\right)+2^{10} 3^{2} x^{2}(4\theta+3)(1732\theta^3+4475\theta^2+3531\theta+645)-2^{14} 3^{4} 17^{2} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 744, 1731240, 5192436480, 17479541356200, ... --> OEIS Normalized instanton numbers (n0=1): 964, -111140, 85888580/3, -9197858184, 3544241969952, ... ; Common denominator:...
\(-(4624z-1)(-1+4608z)^2\)
| \(0\) | \(\frac{ 1}{ 4624}\) | \(\frac{ 1}{ 4608}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 4}\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 4}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 7}{ 4}\) |
| \(0\) | \(2\) | \(\frac{ 3}{ 2}\) | \(\frac{ 9}{ 4}\) |
5
New Number: 3.6 | AESZ: ~33 | Superseeker: 196 2993772 | Hash: 29aeacb8c7e91c8c2838e65ce2750b5a
Degree: 3
\(\theta^4+2^{2} x\left(60\theta^4-8\theta^3+31\theta^2+35\theta+6\right)-2^{10} x^{2}(4\theta+3)(132\theta^3+395\theta^2+363\theta+69)-2^{14} 7^{2} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -24, 13992, -920832, 1808021160, ... --> OEIS Normalized instanton numbers (n0=1): 196, 17212, 2993772, 789858520, 260782261024, ... ; Common denominator:...
\(-(784z-1)(1+512z)^2\)
| \(-\frac{ 1}{ 512}\) | \(0\) | \(\frac{ 1}{ 784}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 4}\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(0\) | \(1\) | \(\frac{ 7}{ 4}\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(2\) | \(\frac{ 9}{ 4}\) |