1
New Number: 6.25 | AESZ: | Superseeker: -11/13 -385/39 | Hash: 47050ee8c9a3655ea77ba8df999a7459
Degree: 6
\(13^{6} \theta^4+13^{5} x(48\theta^2+48\theta+11)(3\theta^2+3\theta+1)-13^{4} x^{2}\left(20766\theta^4+83064\theta^3+129875\theta^2+93622\theta+26145\right)+13^{3} x^{3}\left(1368558\theta^4+8211348\theta^3+18296041\theta^2+17937057\theta+6515866\right)-13^{2} x^{4}\left(48595515\theta^4+388764120\theta^3+1109406129\theta^2+1327511556\theta+560261752\right)+7 13 31 229 x^{5}(\theta+4)(\theta+1)(19935\theta^2+99675\theta+113198)-2^{2} 7^{2} 31^{2} 229^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -11/13, 2149/169, -279167/2197, 42641173/28561, ... --> OEIS Normalized instanton numbers (n0=1): -11/13, 131/52, -385/39, 672/13, -4437/13, ... ; Common denominator:...
\(-(28z-13)(1603z^2-559z+169)(220069z^3-108004z^2+36335z+2197)\)
| ≈\(-0.051688\) | \(0\) | \(\frac{ 559}{ 3206}-\frac{ 507}{ 3206}\sqrt{ 3}I\) | \(\frac{ 559}{ 3206}+\frac{ 507}{ 3206}\sqrt{ 3}I\) | ≈\(0.27123-0.345803I\) | ≈\(0.27123+0.345803I\) | \(\frac{ 13}{ 28}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(4\) |
| \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(5\) |
2
New Number: 8.35 | AESZ: 326 | Superseeker: 11/13 385/39 | Hash: 946b91838924db64fe0ebdf0d473e621
Degree: 8
\(13^{2} \theta^4-13 x\theta(56\theta^3+178\theta^2+115\theta+26)-x^{2}\left(28466\theta^4+109442\theta^3+165603\theta^2+117338\theta+32448\right)-x^{3}\left(233114\theta^4+1257906\theta^3+2622815\theta^2+2467842\theta+872352\right)-x^{4}\left(989585\theta^4+6852298\theta^3+17737939\theta^2+19969754\theta+8108448\right)-x^{5}(\theta+1)(2458967\theta^3+18007287\theta^2+44047582\theta+35386584)-3^{2} x^{6}(\theta+1)(\theta+2)(393163\theta^2+2539029\theta+4164444)-3^{3} 11 x^{7}(\theta+3)(\theta+2)(\theta+1)(8683\theta+34604)-3^{3} 11^{2} 13 17 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 12, 96, 1116, ... --> OEIS Normalized instanton numbers (n0=1): 11/13, 30/13, 385/39, 672/13, 4437/13, ... ; Common denominator:...
\(-(3z+1)(13z^2+5z+1)(153z^3+75z^2+14z-1)(13+11z)^2\)
| \(-\frac{ 13}{ 11}\) | \(-\frac{ 1}{ 3}\) | ≈\(-0.272124-0.216493I\) | ≈\(-0.272124+0.216493I\) | \(-\frac{ 5}{ 26}-\frac{ 3}{ 26}\sqrt{ 3}I\) | \(-\frac{ 5}{ 26}+\frac{ 3}{ 26}\sqrt{ 3}I\) | \(0\) | ≈\(0.054052\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) |