1
New Number: 5.108 | AESZ: 365 | Superseeker: 4 1268 | Hash: f84624e83cd4eb2cc90693bd5627efcf
Degree: 5
\(\theta^4-2^{2} x\left(99\theta^4+78\theta^3+65\theta^2+26\theta+4\right)+2^{6} x^{2}\left(938\theta^4+1382\theta^3+1269\theta^2+554\theta+92\right)-2^{10} x^{3}\left(4171\theta^4+8736\theta^3+8690\theta^2+3948\theta+680\right)+2^{15} 5 x^{4}(2\theta+1)(418\theta^3+951\theta^2+846\theta+260)-2^{19} 3 5^{2} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 720, 44800, 3245200, ... --> OEIS Normalized instanton numbers (n0=1): 4, 107/2, 1268, 89439/4, 396908, ... ; Common denominator:...
\(-(108z-1)(2048z^2-128z+1)(-1+80z)^2\)
| \(0\) | \(\frac{ 1}{ 32}-\frac{ 1}{ 64}\sqrt{ 2}\) | \(\frac{ 1}{ 108}\) | \(\frac{ 1}{ 80}\) | \(\frac{ 1}{ 32}+\frac{ 1}{ 64}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 2}{ 3}\) |
| \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(\frac{ 4}{ 3}\) |
| \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
2
New Number: 5.5 | AESZ: 22 | Superseeker: 10/7 295/7 | Hash: 5b96eae0872756be1130d4b12ffe60a6
Degree: 5
\(7^{2} \theta^4-7 x\left(155\theta^4+286\theta^3+234\theta^2+91\theta+14\right)-x^{2}\left(16105\theta^4+68044\theta^3+102261\theta^2+66094\theta+15736\right)+2^{3} x^{3}\left(2625\theta^4+8589\theta^3+9071\theta^2+3759\theta+476\right)-2^{4} x^{4}\left(465\theta^4+1266\theta^3+1439\theta^2+806\theta+184\right)+2^{9} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 2, 34, 488, 9826, ... --> OEIS Normalized instanton numbers (n0=1): 10/7, 65/7, 295/7, 3065/7, 4245, ... ; Common denominator:...
\((32z-1)(z^2-11z-1)(4z-7)^2\)
| \(\frac{ 11}{ 2}-\frac{ 5}{ 2}\sqrt{ 5}\) | \(0\) | \(\frac{ 1}{ 32}\) | \(\frac{ 7}{ 4}\) | \(\frac{ 11}{ 2}+\frac{ 5}{ 2}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) |
3
New Number: 8.14 | AESZ: 176 | Superseeker: 24 15448/3 | Hash: e2a40a57f7e88dba6655d936b4abe327
Degree: 8
\(\theta^4-2^{2} x(3\theta^2+3\theta+1)(17\theta^2+17\theta+6)+2^{5} x^{2}\left(325\theta^4+2164\theta^3+3053\theta^2+1778\theta+420\right)+2^{10} 3^{2} x^{3}\left(51\theta^4-306\theta^3-934\theta^2-717\theta-204\right)-2^{14} 3^{2} x^{4}\left(397\theta^4+794\theta^3-1454\theta^2-1851\theta-666\right)+2^{18} 3^{4} x^{5}\left(51\theta^4+510\theta^3+290\theta^2-29\theta-64\right)+2^{21} 3^{4} x^{6}\left(325\theta^4-864\theta^3-1489\theta^2-864\theta-144\right)-2^{26} 3^{6} x^{7}(3\theta^2+3\theta+1)(17\theta^2+17\theta+6)+2^{32} 3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 24, 840, 34944, 1618344, ... --> OEIS Normalized instanton numbers (n0=1): 24, -509/2, 15448/3, -128530, 3746624, ... ; Common denominator:...
\((72z-1)(36z-1)(64z-1)(32z-1)(48z-1)^2(48z+1)^2\)
| \(-\frac{ 1}{ 48}\) | \(0\) | \(\frac{ 1}{ 72}\) | \(\frac{ 1}{ 64}\) | \(\frac{ 1}{ 48}\) | \(\frac{ 1}{ 36}\) | \(\frac{ 1}{ 32}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(2\) | \(1\) |