1
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:...
\(-(-1+13z+827z^2+1928z^3+64z^4)(3+22z+12z^2)^2\)
| \(-\frac{ 11}{ 12}-\frac{ 1}{ 12}\sqrt{ 85}\) | \(-\frac{ 11}{ 12}+\frac{ 1}{ 12}\sqrt{ 85}\) | \(0\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(3\) | \(3\) | \(0\) | \(1\) | \(1\) |
| \(4\) | \(4\) | \(0\) | \(2\) | \(1\) |
2
New Number: 8.60 | AESZ: | Superseeker: 247 3584909 | Hash: 540ab51629d98ae18b7d061824bd258b
Degree: 8
\(\theta^4-x\left(1182\theta^4+2172\theta^3+1519\theta^2+433\theta+46\right)+x^{2}\left(70937\theta^4+62468\theta^3-34151\theta^2-26294\theta-4528\right)-2^{3} x^{3}\left(140935\theta^4-41718\theta^3-83276\theta^2-29367\theta-3376\right)+2^{4} 3 x^{4}\left(21007\theta^4-134418\theta^3-100578\theta^2-26137\theta-1974\right)+2^{6} x^{5}\left(29420\theta^4+79292\theta^3-91933\theta^2-88917\theta-22012\right)-2^{6} x^{6}\left(17519\theta^4-73056\theta^3-66923\theta^2-16512\theta+1436\right)-2^{9} 5 x^{7}\left(351\theta^4+510\theta^3+176\theta^2-79\theta-46\right)-2^{12} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 46, 15670, 8332840, 5425831846, ... --> OEIS Normalized instanton numbers (n0=1): 247, 38017/2, 3584909, 2039721503/2, 359173241174, ... ; Common denominator:...
\(-(z+1)(64z^3+600z^2+1119z-1)(1-32z+40z^2)^2\)
| ≈\(-6.805514\) | ≈\(-2.570379\) | \(-1\) | \(0\) | ≈\(0.000893\) | \(\frac{ 2}{ 5}-\frac{ 3}{ 20}\sqrt{ 6}\) | \(\frac{ 2}{ 5}+\frac{ 3}{ 20}\sqrt{ 6}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) | \(1\) |