1
New Number: 4.66 | AESZ: 300 | Superseeker: -1616 -283183120 | Hash: edc54887effd2ebcaa636dcc93baf0b7
Degree: 4
\(\theta^4+2^{4} x\left(371\theta^4+862\theta^3+591\theta^2+160\theta+15\right)+2^{11} 5 x^{2}\left(224\theta^4+2069\theta^3+3277\theta^2+1363\theta+159\right)-2^{16} 5^{2} x^{3}\left(2089\theta^4+7500\theta^3+5533\theta^2+1500\theta+135\right)+2^{23} 5^{3} x^{4}(5\theta+1)(5\theta+2)(5\theta+3)(5\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -240, 378000, -941740800, 2908743037200, ... --> OEIS Normalized instanton numbers (n0=1): -1616, 265534, -283183120, 351860487150, -525536710386800, ... ; Common denominator:...
\((6400000z^2+6576z+1)(-1+320z)^2\)
| ≈\(-0.000842\) | ≈\(-0.000186\) | \(0\) | \(s_2\) | \(s_1\) | \(\frac{ 1}{ 320}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 5}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 2}{ 5}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(3\) | \(\frac{ 3}{ 5}\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(4\) | \(\frac{ 4}{ 5}\) |
2
New Number: 5.118 | AESZ: 416 | Superseeker: 1312 127846048 | Hash: 3ae3241981d64d9c9cc38b29974fa202
Degree: 5
\(\theta^4+2^{4} x\left(560\theta^4-32\theta^3+56\theta^2+72\theta+15\right)+2^{15} x^{2}\left(896\theta^4+272\theta^3+604\theta^2+196\theta+21\right)+2^{24} 3^{2} x^{3}\left(288\theta^4+352\theta^3+364\theta^2+164\theta+29\right)+2^{35} 3^{3} x^{4}(2\theta+1)(16\theta^3+32\theta^2+28\theta+9)+2^{46} 3^{3} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -240, 118032, -72810240, 50454043920, ... --> OEIS Normalized instanton numbers (n0=1): 1312, -301376, 127846048, -70845744192, 45645879602784, ... ; Common denominator:...
\((1+768z)(1024z+1)^2(3072z+1)^2\)
| \(-\frac{ 1}{ 768}\) | \(-\frac{ 1}{ 1024}\) | \(-\frac{ 1}{ 3072}\) | \(0\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(1\) |
| \(2\) | \(1\) | \(4\) | \(0\) | \(\frac{ 3}{ 2}\) |
3
New Number: 5.123 | AESZ: | Superseeker: 96 266464 | Hash: b9a4a4eae678c9ce13a407517f92c30e
Degree: 5
\(\theta^4+2^{4} x\left(28\theta^4-40\theta^3-28\theta^2-8\theta-1\right)+2^{13} x^{2}\left(6\theta^4-12\theta^3+17\theta^2+10\theta+2\right)+2^{18} x^{3}\left(12\theta^4+72\theta^3+35\theta^2-3\theta-4\right)+2^{26} x^{4}(2\theta+1)(4\theta^3-6\theta^2-15\theta-7)-2^{34} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, -240, -24320, 2075920, ... --> OEIS Normalized instanton numbers (n0=1): 96, -4200, 266464, -20295944, 1778341408, ... ; Common denominator:...
\(-(64z-1)(16384z^2+1)(1+256z)^2\)
| \(-\frac{ 1}{ 256}\) | \(0-\frac{ 1}{ 128}I\) | \(0\) | \(0+\frac{ 1}{ 128}I\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
4
New Number: 12.8 | AESZ: | Superseeker: 288 12718752 | Hash: 3373bbe821cc39369e8ba8c46ec88532
Degree: 12
\(\theta^4+2^{4} 3 x\left(112\theta^4+32\theta^3+40\theta^2+24\theta+5\right)+2^{13} x^{2}\left(1408\theta^4+1312\theta^3+1596\theta^2+784\theta+165\right)+2^{22} 3 x^{3}\left(988\theta^4+2088\theta^3+2591\theta^2+1485\theta+372\right)+2^{28} x^{4}\left(24464\theta^4+111040\theta^3+165136\theta^2+111992\theta+31983\right)+2^{38} 3^{2} x^{5}\left(288\theta^4+6544\theta^3+13980\theta^2+11216\theta+3605\right)-2^{46} x^{6}\left(14528\theta^4-36480\theta^3-205340\theta^2-205716\theta-76023\right)-2^{55} 3 x^{7}\left(4848\theta^4+13680\theta^3-20224\theta^2-34444\theta-16035\right)-2^{64} 3^{2} x^{8}\left(384\theta^4+4704\theta^3+2868\theta^2-852\theta-1307\right)+2^{74} 3 x^{9}\left(388\theta^4-1800\theta^3-3283\theta^2-2097\theta-333\right)+2^{80} 3^{2} x^{10}\left(784\theta^4+1184\theta^3+240\theta^2-592\theta-297\right)+2^{93} 3^{3} x^{11}(4\theta^2+8\theta+5)(\theta+1)^2+2^{100} 3^{2} x^{12}(\theta+2)(\theta+1)(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -240, 68880, -22281984, 7875829008, ... --> OEIS Normalized instanton numbers (n0=1): 288, -71872, 12718752, -4499223616, 1510063178336, ... ; Common denominator:...
\((1+768z+65536z^2)(256z+1)^2(512z+1)^2(201326592z^3-1536z-1)^2\)
| \(-\frac{ 3}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\) | \(-\frac{ 1}{ 256}\) | ≈\(-0.002348\) | \(-\frac{ 1}{ 512}\) | \(-\frac{ 3}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\) | ≈\(-0.000695\) | \(0\) | ≈\(0.003043\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) | \(0\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(1\) | \(4\) | \(1\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) |