1
New Number: 5.6 | AESZ: 23 | Superseeker: 4/3 44/3 | Hash: 65760d446ba9c3da587ce5bd9912745e
Degree: 5
\(3^{2} \theta^4-2^{2} 3 x\left(64\theta^4+80\theta^3+73\theta^2+33\theta+6\right)+2^{7} x^{2}\left(194\theta^4+440\theta^3+527\theta^2+315\theta+75\right)-2^{12} x^{3}\left(94\theta^4+288\theta^3+397\theta^2+261\theta+66\right)+2^{17} x^{4}\left(22\theta^4+80\theta^3+117\theta^2+77\theta+19\right)-2^{23} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 104, 1664, 30376, ... --> OEIS Normalized instanton numbers (n0=1): 4/3, 13/3, 44/3, 278/3, 2336/3, ... ; Common denominator:...
\(-(-1+32z)(16z-1)^2(32z-3)^2\)
| \(0\) | \(\frac{ 1}{ 32}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 3}{ 32}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(1\) |
| \(0\) | \(2\) | \(1\) | \(4\) | \(1\) |
2
New Number: 6.34 | AESZ: | Superseeker: 4/3 -124/81 | Hash: 1153f8807d42d96ede28f7a8d06c144b
Degree: 6
\(3^{2} \theta^4-2^{2} 3 x\left(8\theta^4+16\theta^3+27\theta^2+19\theta+5\right)-2^{4} x^{2}\left(272\theta^4+1088\theta^3+1984\theta^2+1792\theta+621\right)+2^{8} x^{3}\left(192\theta^4+1152\theta^3+3448\theta^2+5160\theta+3101\right)+2^{12} x^{4}\left(112\theta^4+896\theta^3+2432\theta^2+2560\theta+753\right)-2^{16} x^{5}\left(96\theta^4+960\theta^3+3860\theta^2+7300\theta+5389\right)+2^{24} x^{6}\left((\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 20/3, 332/3, 13360/27, 966020/81, ... --> OEIS Normalized instanton numbers (n0=1): 4/3, -14/9, -124/81, -4498/243, 37024/729, ... ; Common denominator:...
\((16z-1)^2(16z-3)^2(16z+1)^2\)
| \(-\frac{ 1}{ 16}\) | \(0\) | \(\frac{ 1}{ 16}\) | \(\frac{ 3}{ 16}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(3\) |
| \(0\) | \(0\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) |
| \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(-2\) | \(3\) |
| \(1\) | \(0\) | \(1\) | \(3\) | \(3\) |
3
New Number: 7.19 | AESZ: | Superseeker: 4/3 -124/81 | Hash: f7f0f5d883101c38ed22cb74c80c8f5c
Degree: 7
\(3^{3} \theta^4-2^{2} 3^{2} x\left(12\theta^4-16\theta^3-21\theta^2-13\theta-3\right)-2^{4} 3 x^{2}\left(240\theta^4+1280\theta^3+2068\theta^2+1636\theta+489\right)+2^{10} x^{3}\left(212\theta^4+592\theta^3+490\theta^2-34\theta-129\right)+2^{13} x^{4}\left(72\theta^4+1536\theta^3+4804\theta^2+5468\theta+2031\right)-2^{18} x^{5}\left(100\theta^4+720\theta^3+1535\theta^2+1155\theta+276\right)+2^{20} x^{6}\left(144\theta^4+768\theta^3+1268\theta^2+884\theta+229\right)-2^{28} x^{7}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -4, 68, -496, 9796, ... --> OEIS Normalized instanton numbers (n0=1): 4/3, -14/9, -124/81, -4498/243, 37024/729, ... ; Common denominator:...
\(-(16z-1)^2(16z+1)^2(16z-3)^3\)
| \(-\frac{ 1}{ 16}\) | \(0\) | \(\frac{ 1}{ 16}\) | \(\frac{ 3}{ 16}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(0\) | \(\frac{ 1}{ 2}\) | \(2\) | \(1\) |
| \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(5\) | \(1\) |
4
New Number: 8.33 | AESZ: 322 | Superseeker: 4/3 95/3 | Hash: a19da26bf1a7748e3b7e6151e803da30
Degree: 8
\(3^{2} \theta^4+3 x\left(5\theta^4-122\theta^3-100\theta^2-39\theta-6\right)-x^{2}\left(5052+23736\theta+41729\theta^2+32600\theta^3+8603\theta^4\right)-2^{2} x^{3}\left(33304\theta^4+108297\theta^3+122347\theta^2+61470\theta+11712\right)-2^{2} x^{4}\left(180401\theta^4+547606\theta^3+638125\theta^2+339248\theta+69036\right)-2^{4} x^{5}\left(94934\theta^4+298745\theta^3+355667\theta^2+189660\theta+38224\right)-2^{4} x^{6}\left(73291\theta^4+204216\theta^3+190453\theta^2+68916\theta+6964\right)-2^{7} 3 x^{7}\left(811\theta^4+1886\theta^3+1804\theta^2+861\theta+174\right)-2^{10} 3^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 2, 46, 632, 16846, ... --> OEIS Normalized instanton numbers (n0=1): 4/3, 18, 95/3, 14575/12, 18158/3, ... ; Common denominator:...
\(-(-1+13z+827z^2+1928z^3+64z^4)(3+22z+12z^2)^2\)
| \(-\frac{ 11}{ 12}-\frac{ 1}{ 12}\sqrt{ 85}\) | \(-\frac{ 11}{ 12}+\frac{ 1}{ 12}\sqrt{ 85}\) | \(0\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(3\) | \(3\) | \(0\) | \(1\) | \(1\) |
| \(4\) | \(4\) | \(0\) | \(2\) | \(1\) |