1
New Number: 4.45 | AESZ: 233 | Superseeker: 80 104976 | Hash: 03f67459f6d678669f766c99281b1e79
Degree: 4
\(\theta^4-2^{4} x\left(83\theta^4+94\theta^3+71\theta^2+24\theta+3\right)+2^{11} 3 x^{2}\left(101\theta^4+191\theta^3+174\theta^2+71\theta+10\right)-2^{16} 3^{2} x^{3}\left(203\theta^4+432\theta^3+333\theta^2+102\theta+11\right)+2^{23} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 48, 9360, 2553600, 813027600, ... --> OEIS Normalized instanton numbers (n0=1): 80, 2794, 104976, 5367454, 508265072, ... ; Common denominator:...
\((512z-1)(432z-1)(-1+192z)^2\)
| \(0\) | \(\frac{ 1}{ 512}\) | \(\frac{ 1}{ 432}\) | \(\frac{ 1}{ 192}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(2\) | \(2\) | \(4\) | \(\frac{ 2}{ 3}\) |
2
New Number: 6.37 | AESZ: | Superseeker: 80 249872 | Hash: 0c2998041752cbd976fcc2e18f2072ad
Degree: 6
\(\theta^4-2^{4} x\left(6\theta^4+96\theta^3+99\theta^2+51\theta+11\right)-2^{9} x^{2}\left(222\theta^4+48\theta^3-873\theta^2-897\theta-328\right)+2^{14} x^{3}\left(454\theta^4+6168\theta^3+4887\theta^2+891\theta-651\right)+2^{19} x^{4}\left(6492\theta^4+8760\theta^3-1557\theta^2-6945\theta-2438\right)-2^{28} 7 x^{5}\left(60\theta^4+336\theta^3+693\theta^2+642\theta+227\right)-2^{33} 7^{2} x^{6}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 176, 35792, 7805184, 1768710928, ... --> OEIS Normalized instanton numbers (n0=1): 80, -4222, 249872, -22251117, 2195810928, ... ; Common denominator:...
\(-(32z+1)(64z-1)(224z+1)^2(256z-1)^2\)
| \(-\frac{ 1}{ 32}\) | \(-\frac{ 1}{ 224}\) | \(0\) | \(\frac{ 1}{ 256}\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(4\) | \(0\) | \(\frac{ 3}{ 2}\) | \(2\) | \(\frac{ 3}{ 2}\) |
3
New Number: 8.56 | AESZ: | Superseeker: 80 266256 | Hash: b561c9f1501dce5c055c95391a2176d3
Degree: 8
\(\theta^4-2^{4} x\left(34\theta^4+44\theta^3+31\theta^2+9\theta+1\right)+2^{9} x^{2}\left(94\theta^4-14\theta^3-168\theta^2-98\theta-19\right)-2^{12} x^{3}\left(368\theta^4-1104\theta^3-1505\theta^2-549\theta-60\right)+2^{16} x^{4}\left(28\theta^4-2740\theta^3-154\theta^2+928\theta+331\right)+2^{20} x^{5}\left(678\theta^4+1116\theta^3-2997\theta^2-2295\theta-505\right)-2^{26} x^{6}\left(94\theta^4-561\theta^3-508\theta^2-132\theta+6\right)-2^{28} 5 x^{7}\left(92\theta^4+160\theta^3+97\theta^2+17\theta-2\right)-2^{32} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 2512, 533248, 138259216, ... --> OEIS Normalized instanton numbers (n0=1): 80, 3554, 266256, 31532007, 4663446128, ... ; Common denominator:...
\(-(16z+1)(4096z^3+4864z^2+432z-1)(1-64z+1280z^2)^2\)
| ≈\(-1.090586\) | ≈\(-0.099171\) | \(-\frac{ 1}{ 16}\) | \(0\) | ≈\(0.002257\) | \(\frac{ 1}{ 40}-\frac{ 1}{ 80}I\) | \(\frac{ 1}{ 40}+\frac{ 1}{ 80}I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) | \(1\) |