1
New Number: 12.16 | AESZ: | Superseeker: 288 -8252768 | Hash: e5412f8624ff9afc10459abda2d297d0
Degree: 12
\(\theta^4-2^{4} x\left(160\theta^4+224\theta^3+200\theta^2+88\theta+17\right)+2^{12} x^{2}\left(992\theta^4+1184\theta^3+1664\theta^2+1368\theta+399\right)-2^{22} x^{3}\left(1172\theta^4+1104\theta^3+542\theta^2+912\theta+331\right)+2^{28} x^{4}\left(16624\theta^4+15104\theta^3+5408\theta^2-752\theta-1829\right)-2^{37} x^{5}\left(23072\theta^4+16784\theta^3+23748\theta^2+1100\theta-4281\right)+2^{47} x^{6}\left(12696\theta^4+8556\theta^3+18218\theta^2+6591\theta+144\right)-2^{52} x^{7}\left(167440\theta^4+175808\theta^3+289048\theta^2+160176\theta+37033\right)+2^{61} x^{8}\left(96496\theta^4+172672\theta^3+241896\theta^2+158752\theta+44823\right)-2^{70} x^{9}\left(36784\theta^4+100224\theta^3+148008\theta^2+108576\theta+32891\right)+2^{79} x^{10}\left(8720\theta^4+32704\theta^3+54968\theta^2+44784\theta+14529\right)-2^{91} x^{11}\left(144\theta^4+696\theta^3+1352\theta^2+1222\theta+427\right)+2^{99} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 272, 85264, 30040320, 11678489872, ... --> OEIS Normalized instanton numbers (n0=1): 288, 59200, -8252768, -1223488576, 585571467872, ... ; Common denominator:...
\((512z-1)(65536z^2-768z+1)(134217728z^3-655360z^2+256z-1)^2(256z-1)^3\)
| \(0\) | ≈\(3.7e-05-0.001244I\) | ≈\(3.7e-05+0.001244I\) | \(\frac{ 3}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\) | \(\frac{ 1}{ 512}\) | \(\frac{ 1}{ 256}\) | ≈\(0.004808\) | \(\frac{ 3}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(3\) | \(3\) | \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(4\) | \(4\) | \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
2
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:...
\((1+768z+65536z^2)(256z+1)^2(512z+1)^2(201326592z^3-1536z-1)^2\)
| \(-\frac{ 3}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\) | \(-\frac{ 1}{ 256}\) | ≈\(-0.002348\) | \(-\frac{ 1}{ 512}\) | \(-\frac{ 3}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\) | ≈\(-0.000695\) | \(0\) | ≈\(0.003043\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) | \(0\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(1\) | \(4\) | \(1\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) |
3
New Number: 13.2 | AESZ: | Superseeker: 288 -8252768 | Hash: ad47c122958add1c452a9858793ef177
Degree: 13
\(\theta^4-2^{4} x\left(192\theta^4+352\theta^3+392\theta^2+216\theta+49\right)+2^{12} x^{2}\left(1312\theta^4+2912\theta^3+5328\theta^2+4968\theta+1777\right)-2^{21} x^{3}\left(3336\theta^4+7360\theta^3+12252\theta^2+14040\theta+6269\right)+2^{28} x^{4}\left(26000\theta^4+61440\theta^3+92496\theta^2+79216\theta+30659\right)-2^{38} x^{5}\left(19848\theta^4+49192\theta^3+87106\theta^2+61486\theta+15137\right)+2^{46} x^{6}\left(48464\theta^4+126184\theta^3+248968\theta^2+204418\theta+60711\right)-2^{52} x^{7}\left(370576\theta^4+1125248\theta^3+2210040\theta^2+2071840\theta+776313\right)+2^{64} x^{8}\left(32992\theta^4+127280\theta^3+257876\theta^2+261776\theta+109291\right)-2^{71} x^{9}\left(66640\theta^4+329440\theta^3+743448\theta^2+827560\theta+373765\right)+2^{81} x^{10}\left(11376\theta^4+70016\theta^3+181088\theta^2+224296\theta+110253\right)-2^{88} x^{11}\left(9872\theta^4+73152\theta^3+216216\theta^2+297488\theta+159121\right)+2^{99} x^{12}\left(304\theta^4+2640\theta^3+8824\theta^2+13396\theta+7763\right)-2^{108} x^{13}\left((2\theta+5)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 784, 486672, 279216384, 154637278480, ... --> OEIS Normalized instanton numbers (n0=1): 288, 59200, -8252768, -1223488576, 585571467872, ... ; Common denominator:...
\(-(1-768z+65536z^2)(512z-1)^2(134217728z^3-655360z^2+256z-1)^2(256z-1)^3\)
| \(0\) | ≈\(3.7e-05-0.001244I\) | ≈\(3.7e-05+0.001244I\) | \(\frac{ 3}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\) | \(\frac{ 1}{ 512}\) | \(\frac{ 1}{ 256}\) | ≈\(0.004808\) | \(\frac{ 3}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(0\) | \(0\) | \(1\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(3\) | \(3\) | \(1\) | \(-1\) | \(0\) | \(3\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(4\) | \(4\) | \(2\) | \(1\) | \(0\) | \(4\) | \(2\) | \(\frac{ 5}{ 2}\) |