1
New Number: 3.3 | AESZ: 228 | Superseeker: -68 -18628/3 | Hash: b15f49e2c20021dbc50eaf05a6fd3126
Degree: 3
\(\theta^4+2^{2} x\left(176\theta^4+352\theta^3+289\theta^2+113\theta+18\right)+2^{11} x^{2}\left(80\theta^4+320\theta^3+449\theta^2+258\theta+54\right)+2^{16} 3 x^{3}(2\theta+5)(2\theta+1)(4\theta+3)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -72, 10152, -1739520, 327839400, ... --> OEIS Normalized instanton numbers (n0=1): -68, -835, -18628/3, 359052, 23710944, ... ; Common denominator:...
\((192z+1)(1+256z)^2\)
| \(-\frac{ 1}{ 192}\) | \(-\frac{ 1}{ 256}\) | \(0\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 9}{ 4}\) |
| \(2\) | \(1\) | \(0\) | \(\frac{ 5}{ 2}\) |
2
New Number: 4.74 | AESZ: 363 | Superseeker: -207 621972 | Hash: 15f3be0c25c6a6ea1d78414f1cb31713
Degree: 4
\(\theta^4+3^{2} x\left(231\theta^4+318\theta^3+231\theta^2+72\theta+8\right)+2^{3} 3^{5} x^{2}\left(774\theta^4+1854\theta^3+1869\theta^2+768\theta+100\right)+2^{6} 3^{8} x^{3}\left(951\theta^4+2304\theta^3+1740\theta^2+504\theta+50\right)+2^{10} 3^{12} x^{4}(4\theta+1)(2\theta+1)^2(4\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -72, 22680, -9424800, 4199995800, ... --> OEIS Normalized instanton numbers (n0=1): -207, 5544, 621972, -241386048, 59946723846, ... ; Common denominator:...
\((746496z^2+1647z+1)(1+216z)^2\)
| \(-\frac{ 1}{ 216}\) | \(-\frac{ 61}{ 55296}-\frac{ 5}{ 55296}\sqrt{ 15}I\) | \(-\frac{ 61}{ 55296}+\frac{ 5}{ 55296}\sqrt{ 15}I\) | \(0\) | \(s_1\) | \(s_2\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 4}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(\frac{ 3}{ 4}\) |
3
New Number: 5.93 | AESZ: 333 | Superseeker: 1 2668/3 | Hash: dc274781605ee4262d8745e3fa3a8057
Degree: 5
\(\theta^4+x\theta^2(71\theta^2-2\theta-1)+2^{3} 3 x^{2}\left(154\theta^4+334\theta^3+461\theta^2+248\theta+48\right)+2^{6} 3^{2} x^{3}(5\theta+3)(31\theta^3+39\theta^2-25\theta-21)+2^{9} 3^{4} x^{4}(2\theta+1)(2\theta^3-33\theta^2-56\theta-24)-2^{12} 3^{6} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, -72, 1440, 22680, ... --> OEIS Normalized instanton numbers (n0=1): 1, -66, 2668/3, -2774, -167786, ... ; Common denominator:...
\(-(9z-1)(2304z^2+32z+1)(1+24z)^2\)
| \(-\frac{ 1}{ 24}\) | \(-\frac{ 1}{ 144}-\frac{ 1}{ 72}\sqrt{ 2}I\) | \(-\frac{ 1}{ 144}+\frac{ 1}{ 72}\sqrt{ 2}I\) | \(0\) | \(\frac{ 1}{ 9}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(\frac{ 3}{ 2}\) |
4
New Number: 8.82 | AESZ: | Superseeker: 0 -1/3 | Hash: 8bab1ddc8b31cb2c21f01402f27895ce
Degree: 8
\(\theta^4-x\theta(3\theta^3-6\theta^2-4\theta-1)-x^{2}\left(211\theta^4+856\theta^3+1433\theta^2+1184\theta+384\right)+2 x^{3}\left(761\theta^4+3288\theta^3+6477\theta^2+6654\theta+2700\right)+2^{2} x^{4}(\theta+1)(2013\theta^3+17379\theta^2+40726\theta+28548)-2^{3} x^{5}(\theta+1)(15719\theta^3+126105\theta^2+325408\theta+269508)+2^{5} 3^{2} x^{6}(\theta+1)(\theta+2)(1817\theta^2+11967\theta+19631)-2^{7} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(89\theta+350)+2^{9} 3^{3} 43 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 24, -72, 1296, ... --> OEIS Normalized instanton numbers (n0=1): 0, 1/2, -1/3, -1, -2, ... ; Common denominator:...
\((6z-1)(4z-1)(43z^2-13z+1)(12z+1)^2(-1+2z)^2\)
| \(-\frac{ 1}{ 12}\) | \(0\) | \(\frac{ 13}{ 86}-\frac{ 1}{ 86}\sqrt{ 3}I\) | \(\frac{ 13}{ 86}+\frac{ 1}{ 86}\sqrt{ 3}I\) | \(\frac{ 1}{ 6}\) | \(\frac{ 1}{ 4}\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(3\) |
| \(1\) | \(0\) | \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(4\) |