1
New Number: 5.62 | AESZ: 270 | Superseeker: -76/5 -2100 | Hash: 256e3b3a92e3fd332be8b01f71853ea4
Degree: 5
\(5^{2} \theta^4-2^{2} 5 x\left(48\theta^4+192\theta^3+251\theta^2+155\theta+35\right)-2^{4} x^{2}\left(8704\theta^4+28672\theta^3+43664\theta^2+31760\theta+9265\right)+2^{11} x^{3}\left(1792\theta^4+15360\theta^3+36248\theta^2+33240\theta+10795\right)+2^{16} x^{4}\left(2304\theta^4+12288\theta^3+20816\theta^2+14672\theta+3719\right)+2^{30} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 28, 1324, 63856, 3489004, ... --> OEIS Normalized instanton numbers (n0=1): -76/5, 367/5, -2100, 43436, -6582256/5, ... ; Common denominator:...
\((1+64z)(64z+5)^2(64z-1)^2\)
| \(-\frac{ 5}{ 64}\) | \(-\frac{ 1}{ 64}\) | \(0\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(-\frac{ 1}{ 4}\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(\frac{ 5}{ 4}\) | \(1\) |
2
New Number: 12.13 | AESZ: | Superseeker: 92/5 -76/5 | Hash: dba247c75acfa39c7b95fa5054ec0315
Degree: 12
\(5^{2} \theta^4-2^{2} 5 x\left(204\theta^4+456\theta^3+413\theta^2+185\theta+35\right)+2^{4} x^{2}\left(15584\theta^4+68672\theta^3+112204\theta^2+80560\theta+23355\right)-2^{8} x^{3}\left(31248\theta^4+175968\theta^3+412240\theta^2+410040\theta+153195\right)+2^{12} x^{4}\left(51632\theta^4+209728\theta^3+475320\theta^2+630640\theta+291767\right)-2^{17} x^{5}\left(49392\theta^4+140352\theta^3+11864\theta^2-35120\theta-12789\right)+2^{22} 3 x^{6}\left(12592\theta^4+46080\theta^3+11800\theta^2-52224\theta-39545\right)-2^{27} x^{7}\left(20208\theta^4+72192\theta^3+95128\theta^2+2176\theta-35669\right)+2^{32} x^{8}\left(10672\theta^4+18112\theta^3+35960\theta^2+24560\theta+3975\right)-2^{37} x^{9}\left(5904\theta^4+9216\theta^3+9640\theta^2+6720\theta+2709\right)+2^{42} x^{10}\left(2224\theta^4+6464\theta^3+8328\theta^2+5360\theta+1507\right)-2^{47} x^{11}\left(432\theta^4+1920\theta^3+3400\theta^2+2816\theta+915\right)+2^{53} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 28, 876, 30512, 1161964, ... --> OEIS Normalized instanton numbers (n0=1): 92/5, -342/5, -76/5, 75394/5, -2156752/5, ... ; Common denominator:...
\((64z-1)(32z-1)(256z^2-48z+1)(16z-1)^2(32768z^3-1024z^2-32z-5)^2\)
| ≈\(-0.020941-0.040594I\) | ≈\(-0.020941+0.040594I\) | \(0\) | \(\frac{ 1}{ 64}\) | \(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 32}\) | \(\frac{ 1}{ 16}\) | ≈\(0.073133\) | \(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(3\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(4\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(1\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
3
New Number: 6.20 | AESZ: | Superseeker: 0 -1/3 | Hash: 5169c67af7361bf7e6467dabea9612bd
Degree: 6
\(\theta^4+x\left(11\theta+26\theta^3+2+13\theta^4+24\theta^2\right)-x^{2}(141\theta^2+282\theta+296)(\theta+1)^2-2 x^{3}(\theta+2)(\theta+1)(407\theta^2+1221\theta+654)+2^{2} 7 x^{4}(\theta+3)(\theta+1)(389\theta^2+1556\theta+1460)-2^{3} 3 7^{2} x^{5}(\theta+4)(\theta+1)(29\theta^2+145\theta+166)+2^{5} 3 7^{3} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -2, 28, -224, 2464, ... --> OEIS Normalized instanton numbers (n0=1): 0, 1/2, -1/3, -1, -2, ... ; Common denominator:...
\((-1+2z)(4z-1)(21z^2-9z+1)(1+14z)^2\)
| \(-\frac{ 1}{ 14}\) | \(0\) | \(\frac{ 3}{ 14}-\frac{ 1}{ 42}\sqrt{ 3}I\) | \(\frac{ 3}{ 14}+\frac{ 1}{ 42}\sqrt{ 3}I\) | \(\frac{ 1}{ 4}\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(4\) |
| \(1\) | \(0\) | \(2\) | \(2\) | \(2\) | \(2\) | \(5\) |
4
New Number: 7.6 | AESZ: | Superseeker: 1/3 5/3 | Hash: 24ba77c97bc4b46c39a41c77cc1d1ef4
Degree: 7
\(3^{2} \theta^4-3 x\left(112\theta^4+140\theta^3+133\theta^2+63\theta+12\right)+x^{2}\left(4393\theta^4+9340\theta^3+10903\theta^2+6360\theta+1488\right)-2 x^{3}\left(11669\theta^4+27720\theta^3+27019\theta^2+8460\theta-912\right)+2^{2} x^{4}\left(6799\theta^4-10288\theta^3-82183\theta^2-119168\theta-52672\right)+2^{3} 7 x^{5}(\theta+1)(2611\theta^3+15537\theta^2+26998\theta+14360)-2^{6} 7^{2} x^{6}(\theta+1)(\theta+2)(83\theta^2+105\theta-66)-2^{10} 7^{3} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 28, 232, 2188, ... --> OEIS Normalized instanton numbers (n0=1): 1/3, 5/6, 5/3, 19/3, 29, ... ; Common denominator:...
\(-(2z+1)(8z-1)(7z-1)(16z-1)(z+1)(-3+14z)^2\)
| \(-1\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 8}\) | \(\frac{ 1}{ 7}\) | \(\frac{ 3}{ 14}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(2\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(3\) |