1
New Number: 4.44 | AESZ: 232 | Superseeker: 379/5 1364199/5 | Hash: 8d5ff690c87757ed51a092dee764eede
Degree: 4
\(5^{2} \theta^4-5 x\left(2617\theta^4+4658\theta^3+3379\theta^2+1050\theta+120\right)+2^{6} 3 x^{2}\left(673\theta^4-4871\theta^3-10282\theta^2-5410\theta-860\right)+2^{10} 3^{2} x^{3}\left(955\theta^4+4320\theta^3+3477\theta^2+1020\theta+100\right)-2^{17} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 24, 3960, 974400, 292030200, ... --> OEIS Normalized instanton numbers (n0=1): 379/5, 3346, 1364199/5, 177727432/5, 5658116533, ... ; Common denominator:...
\(-(27z+1)(512z-1)(-5+96z)^2\)
| \(-\frac{ 1}{ 27}\) | \(0\) | \(\frac{ 1}{ 512}\) | \(\frac{ 5}{ 96}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) |
| \(2\) | \(0\) | \(2\) | \(4\) | \(\frac{ 2}{ 3}\) |
2
New Number: 5.73 | AESZ: 293 | Superseeker: 20 13188 | Hash: f19eeaee48396d15d7cf7be47d7d48a7
Degree: 5
\(\theta^4-2^{2} x\left(54\theta^4+66\theta^3+49\theta^2+16\theta+2\right)+2^{4} x^{2}\left(417\theta^4-306\theta^3-1219\theta^2-776\theta-154\right)+2^{8} x^{3}\left(166\theta^4+1920\theta^3+1589\theta^2+432\theta+23\right)-2^{12} 7 x^{4}(2\theta+1)(38\theta^3+45\theta^2+12\theta-2)-2^{14} 7^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 528, 45440, 4763920, ... --> OEIS Normalized instanton numbers (n0=1): 20, 867/2, 13188, 609734, 35512476, ... ; Common denominator:...
\(-(16z+1)(256z^2+176z-1)(-1+28z)^2\)
| \(-\frac{ 11}{ 32}-\frac{ 5}{ 32}\sqrt{ 5}\) | \(-\frac{ 1}{ 16}\) | \(0\) | \(-\frac{ 11}{ 32}+\frac{ 5}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 28}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(\frac{ 3}{ 2}\) |
3
New Number: 5.89 | AESZ: 329 | Superseeker: 48 25200 | Hash: 8c526b3b825d5ad6a3d0fb83ee4e6059
Degree: 5
\(\theta^4-2^{4} x\left(8\theta^4+34\theta^3+25\theta^2+8\theta+1\right)-2^{8} x^{2}\left(87\theta^4+150\theta^3+32\theta^2-2\theta-1\right)-2^{12} x^{3}\left(202\theta^4+240\theta^3+211\theta^2+102\theta+19\right)-2^{16} 3 x^{4}(2\theta+1)(22\theta^3+45\theta^2+38\theta+12)-2^{20} 3^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 1200, 136960, 19010320, ... --> OEIS Normalized instanton numbers (n0=1): 48, 270, 25200, 968066, 80892688, ... ; Common denominator:...
\(-(16384z^3+3072z^2+224z-1)(1+48z)^2\)
| ≈\(-0.095858-0.072741I\) | ≈\(-0.095858+0.072741I\) | \(-\frac{ 1}{ 48}\) | \(0\) | ≈\(0.004215\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(\frac{ 3}{ 2}\) |
4
New Number: 1.14 | AESZ: 14 | Superseeker: 1248 683015008 | Hash: 03af56f4ae0cea2c4b219620b08dc49b
Degree: 1
\(\theta^4-2^{4} 3 x(6\theta+1)(2\theta+1)^2(6\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 240, 498960, 1633632000, 6558930378000, ... --> OEIS Normalized instanton numbers (n0=1): 1248, 597192, 683015008, 1149904141056, 2394928461766560, ... ; Common denominator:...
\(1-6912z\)
| \(0\) | \(\frac{ 1}{ 6912}\) | \(\infty\) |
|---|---|---|
| \(0\) | \(0\) | \(\frac{ 1}{ 6}\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(2\) | \(\frac{ 5}{ 6}\) |