1
New Number: 11.7 | AESZ: | Superseeker: 9 2564/3 | Hash: 3933e1482d30ea8bca1e5e5f914286e2
Degree: 11
\(\theta^4+3 x\left(60\theta^4+12\theta^3+19\theta^2+13\theta+3\right)+3^{3} x^{2}\left(463\theta^4+304\theta^3+405\theta^2+184\theta+27\right)+3^{5} x^{3}\left(1710\theta^4+2268\theta^3+2450\theta^2+1080\theta+153\right)+3^{7} x^{4}\left(2870\theta^4+5344\theta^3+4044\theta^2-188\theta-981\right)+3^{9} x^{5}\left(560\theta^4-4552\theta^3-20650\theta^2-29130\theta-13389\right)-3^{11} x^{6}\left(5114\theta^4+37440\theta^3+101098\theta^2+119700\theta+51219\right)-3^{13} x^{7}\left(6620\theta^4+48712\theta^3+130868\theta^2+152172\theta+63981\right)-3^{16} x^{8}(\theta+1)(83\theta^3-2739\theta^2-16257\theta-20563)+3^{17} x^{9}(\theta+1)(\theta+2)(4676\theta^2+42864\theta+94887)+3^{20} x^{10}(\theta+3)(\theta+2)(\theta+1)(505\theta+2522)+2 3^{23} 7 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -9, 135, -2115, 38799, ... --> OEIS Normalized instanton numbers (n0=1): 9, -72, 2564/3, -12924, 228024, ... ; Common denominator:...
\((18z+1)(189z^2+18z+1)(27z+1)^2(9z-1)^2(81z^2+54z+1)^2\)
| \(-\frac{ 1}{ 3}-\frac{ 2}{ 9}\sqrt{ 2}\) | \(-\frac{ 1}{ 18}\) | \(-\frac{ 1}{ 21}-\frac{ 2}{ 63}\sqrt{ 3}I\) | \(-\frac{ 1}{ 21}+\frac{ 2}{ 63}\sqrt{ 3}I\) | \(-\frac{ 1}{ 27}\) | \(-\frac{ 1}{ 3}+\frac{ 2}{ 9}\sqrt{ 2}\) | \(0\) | \(\frac{ 1}{ 9}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(1\) | \(4\) | \(0\) | \(1\) | \(4\) |
2
New Number: 13.11 | AESZ: | Superseeker: 7 -2044/9 | Hash: d6e183df7853fe5068c8b8cdeb3f63cb
Degree: 13
\(\theta^4-x\left(98\theta^4+164\theta^3+137\theta^2+55\theta+9\right)+x^{2}\left(3822\theta^4+11400\theta^3+14901\theta^2+8746\theta+2007\right)-x^{3}\left(64148\theta^4+196344\theta^3+271665\theta^2+199855\theta+60354\right)+x^{4}\left(802771\theta^4+2242504\theta^3+2203855\theta^2+1316868\theta+390636\right)-2 3 x^{5}\left(1040145\theta^4+2982426\theta^3+3578912\theta^2+1897395\theta+345411\right)+2 3^{2} x^{6}\left(1927994\theta^4+4917832\theta^3+7329041\theta^2+5154630\theta+1338003\right)-2 3^{5} x^{7}\left(219316\theta^4+761432\theta^3+1064075\theta^2+703129\theta+181966\right)+3^{4} x^{8}\left(754759\theta^4+7471824\theta^3+13904030\theta^2+8830464\theta+1544112\right)+3^{7} x^{9}\left(174966\theta^4+736236\theta^3+1307237\theta^2+1340471\theta+568265\right)-3^{10} x^{10}(\theta+1)(8018\theta^3+62342\theta^2+139257\theta+108861)-3^{9} x^{11}(\theta+1)(\theta+2)(28988\theta^2+81396\theta+36331)+3^{12} x^{12}(\theta+3)(\theta+2)(\theta+1)(1061\theta+5386)+2 3^{15} 17 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 9, 135, 2115, 18063, ... --> OEIS Normalized instanton numbers (n0=1): 7, -31/4, -2044/9, -1380, -8520, ... ; Common denominator:...
\((2z-1)(4131z^3-2187z^2+81z-1)(3z-1)^2(81z^2-6z+1)^2(z+1)^3\)
| \(-1\) | \(0\) | ≈\(0.019487-0.01067I\) | ≈\(0.019487+0.01067I\) | \(\frac{ 1}{ 27}-\frac{ 2}{ 27}\sqrt{ 2}I\) | \(\frac{ 1}{ 27}+\frac{ 2}{ 27}\sqrt{ 2}I\) | \(\frac{ 1}{ 3}\) | ≈\(0.490438\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(1\) | \(1\) | \(3\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) |
| \(2\) | \(0\) | \(2\) | \(2\) | \(4\) | \(4\) | \(1\) | \(2\) | \(2\) | \(4\) |
3
New Number: 8.11 | AESZ: 162 | Superseeker: 9 242/3 | Hash: 542708b59b898c35f43e00120897ff8d
Degree: 8
\(\theta^4-3 x(3\theta^2+3\theta+1)(10\theta^2+10\theta+3)+3^{3} x^{2}\left(91\theta^4+472\theta^3+659\theta^2+374\theta+81\right)+3^{6} x^{3}\left(30\theta^4-180\theta^3-551\theta^2-417\theta-111\right)-3^{8} x^{4}\left(200\theta^4+400\theta^3-514\theta^2-714\theta-237\right)+3^{11} x^{5}\left(30\theta^4+300\theta^3+169\theta^2-25\theta-35\right)+3^{13} x^{6}\left(91\theta^4-108\theta^3-211\theta^2-108\theta-15\right)-3^{16} x^{7}(3\theta^2+3\theta+1)(10\theta^2+10\theta+3)+3^{20} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 9, 135, 1953, 5751, ... --> OEIS Normalized instanton numbers (n0=1): 9, -153/4, 242/3, -4923, 34245, ... ; Common denominator:...
\((27z^2-9z+1)(2187z^2-81z+1)(-1+243z^2)^2\)
| \(-\frac{ 1}{ 27}\sqrt{ 3}\) | \(0\) | \(\frac{ 1}{ 54}-\frac{ 1}{ 162}\sqrt{ 3}I\) | \(\frac{ 1}{ 54}+\frac{ 1}{ 162}\sqrt{ 3}I\) | \(\frac{ 1}{ 27}\sqrt{ 3}\) | \(\frac{ 1}{ 6}-\frac{ 1}{ 18}\sqrt{ 3}I\) | \(\frac{ 1}{ 6}+\frac{ 1}{ 18}\sqrt{ 3}I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(2\) | \(1\) |
4
New Number: 9.3 | AESZ: | Superseeker: 10 3394/3 | Hash: 40e3715abcc5c4cb07e700ca79f80abf
Degree: 9
\(\theta^4-x\left(57\theta^4+116\theta^3+84\theta^2+26\theta+3\right)-2 x^{2}\left(894\theta^4+3208\theta^3+4571\theta^2+2771\theta+651\right)-2 x^{3}\left(7322\theta^4+56368\theta^3+124783\theta^2+101099\theta+29757\right)+2 3^{2} x^{4}\left(6967\theta^4-27080\theta^3-139991\theta^2-138507\theta-45297\right)+2 3^{4} x^{5}\left(17617\theta^4+49068\theta^3-31255\theta^2-79893\theta-34578\right)+2 3^{8} x^{6}\left(1082\theta^4+8360\theta^3+7967\theta^2+1439\theta-773\right)-2 3^{11} x^{7}\left(198\theta^4-864\theta^3-1545\theta^2-909\theta-155\right)-3^{15} x^{8}\left(69\theta^4+144\theta^3+126\theta^2+54\theta+10\right)-3^{20} x^{9}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 3, 135, 5349, 258039, ... --> OEIS Normalized instanton numbers (n0=1): 10, 77, 3394/3, 24029, 640402, ... ; Common denominator:...
\(-(-1+81z)(-1+9z)^2(81z^2+14z+1)^3\)
| \(-\frac{ 7}{ 81}-\frac{ 4}{ 81}\sqrt{ 2}I\) | \(-\frac{ 7}{ 81}+\frac{ 4}{ 81}\sqrt{ 2}I\) | \(0\) | \(\frac{ 1}{ 81}\) | \(\frac{ 1}{ 9}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(1\) |