1
New Number: 4.27 | AESZ: 189 | Superseeker: -30 -11360 | Hash: 2ce243b7535bf4eefb88252a3c164466
Degree: 4
\(\theta^4-2 x\left(260\theta^4+520\theta^3+625\theta^2+365\theta+82\right)+2^{2} x^{2}\left(17412\theta^4+69648\theta^3+107199\theta^2+75102\theta+20320\right)-2^{4} x^{3}\left(33280\theta^4+199680\theta^3+476760\theta^2+531720\theta+230741\right)+2^{8} x^{4}(8\theta+13)(8\theta+15)(8\theta+17)(8\theta+19)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 164, 32886, 7144704, 1616497596, ... --> OEIS Normalized instanton numbers (n0=1): -30, -885/2, -11360, -365910, -13641180, ... ; Common denominator:...
\((256z-1)^2(4z-1)^2\)
| \(0\) | \(\frac{ 1}{ 256}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 13}{ 8}\) |
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 15}{ 8}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 17}{ 8}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 19}{ 8}\) |
2
New Number: 4.77 | AESZ: | Superseeker: 1 68/9 | Hash: f9623221ffe8be4c1e31a6e6ce195a37
Degree: 4
\(\theta^4-x\left(16+80\theta+161\theta^2+162\theta^3+81\theta^4\right)+2^{3} x^{2}\left(303\theta^4+1212\theta^3+1952\theta^2+1480\theta+440\right)-2^{6} x^{3}(124\theta^2+372\theta+263)(2\theta+3)^2+2^{9} 3 5^{2} x^{4}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 280, 5152, 98200, ... --> OEIS Normalized instanton numbers (n0=1): 1, -2, 68/9, -30, 150, ... ; Common denominator:...
\((25z-1)(24z-1)(-1+16z)^2\)
| \(0\) | \(\frac{ 1}{ 25}\) | \(\frac{ 1}{ 24}\) | \(\frac{ 1}{ 16}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(2\) | \(2\) | \(1\) | \(3\) |
3
New Number: 5.12 | AESZ: 74 | Superseeker: -30 -14632 | Hash: e668180adb7c88d4e5fbab5eb7ee61c7
Degree: 5
\(\theta^4-2 3 x\left(99\theta^4+36\theta^3+39\theta^2+21\theta+4\right)+2^{2} 3^{2} x^{2}\left(3807\theta^4+3564\theta^3+3798\theta^2+1683\theta+284\right)-2^{3} 3^{5} x^{3}\left(7857\theta^4+13608\theta^3+14562\theta^2+7317\theta+1444\right)+2^{4} 3^{9} x^{4}\left(2592\theta^4+7128\theta^3+8550\theta^2+4851\theta+1052\right)-2^{5} 3^{13} x^{5}(3\theta+2)(3\theta+4)(6\theta+5)(6\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 24, 1152, 71520, 5101200, ... --> OEIS Normalized instanton numbers (n0=1): -30, -516, -14632, -4227807/8, -22139868, ... ; Common denominator:...
\(-(-1+54z)(162z-1)^2(108z-1)^2\)
| \(0\) | \(\frac{ 1}{ 162}\) | \(\frac{ 1}{ 108}\) | \(\frac{ 1}{ 54}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 5}{ 6}\) |
| \(0\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 7}{ 6}\) |
| \(0\) | \(4\) | \(1\) | \(2\) | \(\frac{ 4}{ 3}\) |
4
New Number: 8.32 | AESZ: 317 | Superseeker: 69/4 14365/12 | Hash: cda8cce31025f51636125bea67a820d1
Degree: 8
\(2^{4} \theta^4-2^{2} 3 x\left(162\theta^4+414\theta^3+335\theta^2+128\theta+20\right)+3^{3} x^{2}\left(1219\theta^4+10906\theta^3+18963\theta^2+11824\theta+2708\right)+3^{5} 5 x^{3}\left(922\theta^4+162\theta^3-6403\theta^2-6576\theta-1964\right)-3^{7} x^{4}\left(10358\theta^4+58054\theta^3+62251\theta^2+29672\theta+4907\right)-3^{9} 5 x^{5}\left(1519\theta^4-1262\theta^3+1371\theta^2+4264\theta+1802\right)+2 3^{11} 5 x^{6}\left(1727\theta^4+3702\theta^3+3085\theta^2+882\theta+17\right)-3^{13} 5^{2} x^{7}\left(239\theta^4+460\theta^3+314\theta^2+84\theta+6\right)-3^{16} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 15, 459, 19545, 1019259, ... --> OEIS Normalized instanton numbers (n0=1): 69/4, -30, 14365/12, 3015/2, 1376205/4, ... ; Common denominator:...
\(-(27z-1)(243z^3+2214z^2-117z+1)(-4-45z+405z^2)^2\)
| ≈\(-9.163702\) | \(\frac{ 1}{ 18}-\frac{ 1}{ 90}\sqrt{ 105}\) | \(0\) | ≈\(0.010727\) | \(\frac{ 1}{ 27}\) | ≈\(0.041864\) | \(\frac{ 1}{ 18}+\frac{ 1}{ 90}\sqrt{ 105}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(1\) |
5
New Number: 8.55 | AESZ: | Superseeker: 1 68/9 | Hash: 39ed8ce7572bc79a333f77c892033bcf
Degree: 8
\(\theta^4-x\left(33\theta^4+98\theta^3+105\theta^2+56\theta+12\right)+2^{3} x^{2}\left(34\theta^4+276\theta^3+609\theta^2+582\theta+216\right)+2^{4} 3 x^{3}\left(11\theta^4-170\theta^3-941\theta^2-1520\theta-846\right)-2^{7} 3^{2} x^{4}(2\theta^2+6\theta+5)(4\theta^2+12\theta-31)+2^{8} 3 x^{5}\left(11\theta^4+302\theta^3+1183\theta^2+1652\theta+726\right)+2^{11} x^{6}\left(34\theta^4+132\theta^3-39\theta^2-708\theta-747\right)-2^{12} x^{7}\left(33\theta^4+298\theta^3+1005\theta^2+1492\theta+816\right)+2^{16} x^{8}\left((\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 120, 1216, 13080, ... --> OEIS Normalized instanton numbers (n0=1): 1, -2, 68/9, -30, 150, ... ; Common denominator:...
\((z-1)(16z-1)(16z^2-16z+1)(4z-1)^2(4z+1)^2\)
| \(-\frac{ 1}{ 4}\) | \(0\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 2}-\frac{ 1}{ 4}\sqrt{ 3}\) | \(\frac{ 1}{ 4}\) | \(\frac{ 1}{ 2}+\frac{ 1}{ 4}\sqrt{ 3}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(3\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(3\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(3\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(1\) | \(2\) | \(2\) | \(3\) |