1
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:...
\(-(784z-1)(1+512z)^2\)
| \(-\frac{ 1}{ 512}\) | \(0\) | \(\frac{ 1}{ 784}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 4}\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(0\) | \(1\) | \(\frac{ 7}{ 4}\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(2\) | \(\frac{ 9}{ 4}\) |
2
New Number: 5.101 | AESZ: 348 | Superseeker: -52 -44772 | Hash: 8759f016475d17d0fc88f4b98a374d3f
Degree: 5
\(\theta^4+2^{2} x\left(70\theta^4+194\theta^3+145\theta^2+48\theta+6\right)-2^{4} 3 x^{2}\left(141\theta^4-858\theta^3-2111\theta^2-1192\theta-206\right)-2^{8} 3^{2} x^{3}\left(18\theta^4-324\theta^3-2364\theta^2-1953\theta-403\right)-2^{10} 3^{4} x^{4}(3\theta+1)(3\theta+2)(42\theta^2+258\theta+223)+2^{14} 3^{6} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -24, 2160, -309120, 54608400, ... --> OEIS Normalized instanton numbers (n0=1): -52, 461/2, -44772, 3546761/2, -178670332, ... ; Common denominator:...
\((746496z^3+17280z^2+352z+1)(-1+36z)^2\)
| ≈\(-0.009925-0.017537I\) | ≈\(-0.009925+0.017537I\) | ≈\(-0.003299\) | \(0\) | \(\frac{ 1}{ 36}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 2}{ 3}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(3\) | \(\frac{ 4}{ 3}\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(4\) | \(\frac{ 5}{ 3}\) |
3
New Number: 5.41 | AESZ: 230 | Superseeker: 291 7935104 | Hash: ac762b013587176079179af09a110ab6
Degree: 5
\(\theta^4+3 x\left(945\theta^4-162\theta^3-49\theta^2+32\theta+8\right)+2 3^{4} x^{2}\left(17928\theta^4+2970\theta^3+10187\theta^2+3376\theta+408\right)+2^{2} 3^{7} x^{3}\left(156285\theta^4+200016\theta^3+193630\theta^2+84378\theta+13964\right)+2^{4} 3^{10} 19 x^{4}(4743\theta^2+8199\theta+4922)(2\theta+1)^2+2^{9} 3^{15} 19^{2} x^{5}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -24, -648, 494400, -82643400, ... --> OEIS Normalized instanton numbers (n0=1): 291, -38832, 7935104, -2098976940, 651305429796, ... ; Common denominator:...
\((432z+1)(93312z^2+351z+1)(1+1026z)^2\)
| \(-\frac{ 1}{ 432}\) | \(-\frac{ 13}{ 6912}-\frac{ 7}{ 6912}\sqrt{ 7}I\) | \(-\frac{ 13}{ 6912}+\frac{ 7}{ 6912}\sqrt{ 7}I\) | \(-\frac{ 1}{ 1026}\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(\frac{ 3}{ 2}\) |
4
New Number: 6.39 | AESZ: | Superseeker: 8 3784/3 | Hash: 6429f42cbe18bee944ac13edab1fbbcc
Degree: 6
\(\theta^4+2^{2} x\left(49\theta^4+98\theta^3+86\theta^2+37\theta+6\right)+2^{5} x^{2}\left(593\theta^4+2372\theta^3+3521\theta^2+2298\theta+504\right)+2^{10} 3 x^{3}\left(332\theta^4+1992\theta^3+4194\theta^2+3618\theta+945\right)+2^{14} 3^{2} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)+2^{18} 3^{3} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2+2^{21} 3^{4} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -24, 648, -11520, -123480, ... --> OEIS Normalized instanton numbers (n0=1): 8, 39/2, 3784/3, 51036, 1659840, ... ; Common denominator:...
\((24z+1)(110592z^3+6912z^2+108z+1)(1+32z)^2\)
| ≈\(-0.045368\) | \(-\frac{ 1}{ 24}\) | \(-\frac{ 1}{ 32}\) | ≈\(-0.008566-0.011222I\) | ≈\(-0.008566+0.011222I\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(\frac{ 5}{ 2}\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(\frac{ 7}{ 2}\) |
| \(2\) | \(2\) | \(1\) | \(2\) | \(2\) | \(0\) | \(\frac{ 11}{ 2}\) |
5
New Number: 8.80 | AESZ: | Superseeker: -28/3 2764/3 | Hash: 01b1872abfd55652952ae535920a40fe
Degree: 8
\(3^{2} \theta^4+2^{2} 3 x\left(148\theta^4+248\theta^3+223\theta^2+99\theta+18\right)+2^{7} x^{2}\left(1124\theta^4+3080\theta^3+4211\theta^2+2709\theta+675\right)+2^{12} x^{3}\left(1684\theta^4+4872\theta^3+7059\theta^2+5373\theta+1530\right)+2^{17} x^{4}\left(1828\theta^4+4952\theta^3+5125\theta^2+2799\theta+599\right)+2^{23} x^{5}\left(720\theta^4+1992\theta^3+2102\theta^2+691\theta-13\right)+2^{29} x^{6}\left(200\theta^4+504\theta^3+669\theta^2+390\theta+83\right)+2^{35} x^{7}\left(40\theta^4+104\theta^3+118\theta^2+66\theta+15\right)+2^{43} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -24, 872, -37248, 1740456, ... --> OEIS Normalized instanton numbers (n0=1): -28/3, 49/3, 2764/3, 13414, 44384, ... ; Common denominator:...
\((16z+1)(32z+1)(64z+1)^2(2048z^2+32z+3)^2\)
| \(-\frac{ 1}{ 16}\) | \(-\frac{ 1}{ 32}\) | \(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 23}I\) | \(-\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 23}I\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(3\) | \(0\) | \(1\) |
| \(2\) | \(2\) | \(1\) | \(4\) | \(4\) | \(0\) | \(1\) |