1
New Number: 2.10 | AESZ: 70 | Superseeker: 27 18089 | Hash: 3d2adae6eaf26a56c76b8b67d92cc5df
Degree: 2
\(\theta^4-3 x(3\theta+1)(3\theta+2)(10\theta^2+10\theta+3)+3^{4} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 1350, 156240, 22141350, ... --> OEIS Normalized instanton numbers (n0=1): 27, 432, 18089, 997785, 68438142, ... ; Common denominator:...
\((243z-1)(27z-1)\)
\(0\) | \(\frac{ 1}{ 27}\) | \(\frac{ 1}{ 243}\) | \(\infty\) |
---|---|---|---|
\(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 2}{ 3}\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 4}{ 3}\) |
\(0\) | \(2\) | \(2\) | \(\frac{ 5}{ 3}\) |
2
New Number: 2.14 | AESZ: 48 | Superseeker: 24 5832 | Hash: 8081a3989d09a7d612953dac3341d90c
Degree: 2
\(\theta^4-2^{2} 3 x(3\theta+1)(3\theta+2)(3\theta^2+3\theta+1)+2^{5} 3^{2} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 24, 1800, 188160, 23423400, ... --> OEIS Normalized instanton numbers (n0=1): 24, 291/2, 5832, 247116, 12634944, ... ; Common denominator:...
\((216z-1)(108z-1)\)
\(0\) | \(\frac{ 1}{ 108}\) | \(\frac{ 1}{ 216}\) | \(\infty\) |
---|---|---|---|
\(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 2}{ 3}\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 4}{ 3}\) |
\(0\) | \(2\) | \(2\) | \(\frac{ 5}{ 3}\) |
3
New Number: 2.18 | AESZ: 110 | Superseeker: 36 8076 | Hash: 5060b638cac581d5f0f9dd7f40d90e6c
Degree: 2
\(\theta^4-2^{2} 3 x(3\theta+1)(3\theta+2)(8\theta^2+8\theta+3)+2^{8} 3^{2} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 72, 14760, 3951360, 1198751400, ... --> OEIS Normalized instanton numbers (n0=1): 36, -144, 8076, -57996, 6960672, ... ; Common denominator:...
\((432z-1)^2\)
\(0\) | \(\infty\) | \(\frac{ 1}{ 432}\) |
---|---|---|
\(0\) | \(\frac{ 1}{ 3}\) | \(0\) |
\(0\) | \(\frac{ 2}{ 3}\) | \(\frac{ 1}{ 2}\) |
\(0\) | \(\frac{ 4}{ 3}\) | \(\frac{ 1}{ 2}\) |
\(0\) | \(\frac{ 5}{ 3}\) | \(1\) |
4
New Number: 2.21 | AESZ: 134 | Superseeker: 18 -5177 | Hash: cc6d92c4b8a8dadb92b447c54e3a2a2f
Degree: 2
\(\theta^4-3^{2} x(3\theta+1)(3\theta+2)(3\theta^2+3\theta+1)+3^{5} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 810, 35280, 311850, ... --> OEIS Normalized instanton numbers (n0=1): 18, -207/2, -5177, -155979, -923301, ... ; Common denominator:...
\(1-243z+19683z^2\)
\(0\) | \(\frac{ 1}{ 162}+\frac{ 1}{ 486}\sqrt{ 3}I\) | \(\frac{ 1}{ 162}-\frac{ 1}{ 486}\sqrt{ 3}I\) | \(\infty\) |
---|---|---|---|
\(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 2}{ 3}\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 4}{ 3}\) |
\(0\) | \(2\) | \(2\) | \(\frac{ 5}{ 3}\) |
5
New Number: 2.25 | AESZ: 138 | Superseeker: 27 2618 | Hash: c524254b716132352b27914640b03c8b
Degree: 2
\(\theta^4-3 x(3\theta+1)(3\theta+2)(17\theta^2+17\theta+6)+2^{3} 3^{4} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 36, 3780, 524160, 82952100, ... --> OEIS Normalized instanton numbers (n0=1): 27, 189/4, 2618, 43713, 2319057, ... ; Common denominator:...
\((243z-1)(216z-1)\)
\(0\) | \(\frac{ 1}{ 243}\) | \(\frac{ 1}{ 216}\) | \(\infty\) |
---|---|---|---|
\(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 2}{ 3}\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 4}{ 3}\) |
\(0\) | \(2\) | \(2\) | \(\frac{ 5}{ 3}\) |
6
New Number: 2.29 | AESZ: 142 | Superseeker: 45 27735 | Hash: 85c2c2d8111a859d4cc03e8892c56af9
Degree: 2
\(\theta^4-3^{2} x(3\theta+1)(3\theta+2)(18\theta^2+18\theta+7)+3^{8} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 126, 44550, 20447280, 10600093350, ... --> OEIS Normalized instanton numbers (n0=1): 45, -3465/4, 27735, -1156005, 55721970, ... ; Common denominator:...
\((729z-1)^2\)
\(0\) | \(\infty\) | \(\frac{ 1}{ 729}\) |
---|---|---|
\(0\) | \(\frac{ 1}{ 3}\) | \(0\) |
\(0\) | \(\frac{ 2}{ 3}\) | \(\frac{ 1}{ 3}\) |
\(0\) | \(\frac{ 4}{ 3}\) | \(\frac{ 2}{ 3}\) |
\(0\) | \(\frac{ 5}{ 3}\) | \(1\) |
7
New Number: 2.2 | AESZ: 15 | Superseeker: 21 15894 | Hash: c8053e0e9c05ef468263fafd5e3fc764
Degree: 2
\(\theta^4-3 x(3\theta+1)(3\theta+2)(7\theta^2+7\theta+2)-2^{3} 3^{2} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 900, 94080, 11988900, ... --> OEIS Normalized instanton numbers (n0=1): 21, 480, 15894, 894075, 58703151, ... ; Common denominator:...
\(-(27z+1)(216z-1)\)
\(0\) | \(\frac{ 1}{ 216}\) | \(\infty\) | \(-\frac{ 1}{ 27}\) |
---|---|---|---|
\(0\) | \(0\) | \(\frac{ 1}{ 3}\) | \(0\) |
\(0\) | \(1\) | \(\frac{ 2}{ 3}\) | \(1\) |
\(0\) | \(1\) | \(\frac{ 4}{ 3}\) | \(1\) |
\(0\) | \(2\) | \(\frac{ 5}{ 3}\) | \(2\) |
8
New Number: 2.32 | AESZ: | Superseeker: 60 307860 | Hash: c2f30268af49d0bdc6a36f8b0fce3367
Degree: 2
\(\theta^4-2^{2} 3 x(3\theta+1)(3\theta+2)(32\theta^2+32\theta+13)+2^{12} 3^{2} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 312, 268200, 297104640, 370278354600, ... --> OEIS Normalized instanton numbers (n0=1): 60, -7635, 307860, -44194980, 3687387360, ... ; Common denominator:...
\((1728z-1)^2\)
\(0\) | \(\frac{ 1}{ 1728}\) | \(\infty\) |
---|---|---|
\(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
\(0\) | \(\frac{ 1}{ 4}\) | \(\frac{ 2}{ 3}\) |
\(0\) | \(\frac{ 3}{ 4}\) | \(\frac{ 4}{ 3}\) |
\(0\) | \(1\) | \(\frac{ 5}{ 3}\) |
9
New Number: 2.36 | AESZ: | Superseeker: -36 128217204 | Hash: 4dbde07f1392f8d49d0e10858d3a17f1
Degree: 2
\(\theta^4-2^{2} 3^{2} x(3\theta+1)(3\theta+2)(72\theta^2+72\theta+31)+2^{8} 3^{8} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 2232, 13377960, 102324983040, 875961004703400, ... --> OEIS Normalized instanton numbers (n0=1): -36, -486279, 128217204, -74772628524, 63925611915744, ... ; Common denominator:...
\((11664z-1)^2\)
\(0\) | \(\infty\) | \(\frac{ 1}{ 11664}\) |
---|---|---|
\(0\) | \(\frac{ 1}{ 3}\) | \(0\) |
\(0\) | \(\frac{ 2}{ 3}\) | \(\frac{ 1}{ 6}\) |
\(0\) | \(\frac{ 4}{ 3}\) | \(\frac{ 5}{ 6}\) |
\(0\) | \(\frac{ 5}{ 3}\) | \(1\) |
10
New Number: 2.6 | AESZ: 24 | Superseeker: 36 41421 | Hash: 5e8f8f32b5e99693a2956e1240b9fdff
Degree: 2
\(\theta^4-3 x(3\theta+1)(3\theta+2)(11\theta^2+11\theta+3)-3^{2} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 1710, 246960, 43347150, ... --> OEIS Normalized instanton numbers (n0=1): 36, 837, 41421, 2992851, 266362506, ... ; Common denominator:...
\(1-297z-729z^2\)
\(-\frac{ 11}{ 54}-\frac{ 5}{ 54}\sqrt{ 5}\) | \(0\) | \(-\frac{ 11}{ 54}+\frac{ 5}{ 54}\sqrt{ 5}\) | \(\infty\) |
---|---|---|---|
\(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
\(1\) | \(0\) | \(1\) | \(\frac{ 2}{ 3}\) |
\(1\) | \(0\) | \(1\) | \(\frac{ 4}{ 3}\) |
\(2\) | \(0\) | \(2\) | \(\frac{ 5}{ 3}\) |
11
New Number: 5.101 | AESZ: 348 | Superseeker: -52 -44772 | Hash: 8759f016475d17d0fc88f4b98a374d3f
Degree: 5
\(\theta^4+2^{2} x\left(70\theta^4+194\theta^3+145\theta^2+48\theta+6\right)-2^{4} 3 x^{2}\left(141\theta^4-858\theta^3-2111\theta^2-1192\theta-206\right)-2^{8} 3^{2} x^{3}\left(18\theta^4-324\theta^3-2364\theta^2-1953\theta-403\right)-2^{10} 3^{4} x^{4}(3\theta+1)(3\theta+2)(42\theta^2+258\theta+223)+2^{14} 3^{6} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -24, 2160, -309120, 54608400, ... --> OEIS Normalized instanton numbers (n0=1): -52, 461/2, -44772, 3546761/2, -178670332, ... ; Common denominator:...
\((746496z^3+17280z^2+352z+1)(-1+36z)^2\)
\(0\) | \(\infty\) | \(\frac{ 1}{ 36}\) | ≈\(-0.009925+0.017537I\) | ≈\(-0.003299\) | ≈\(-0.009925-0.017537I\) |
---|---|---|---|---|---|
\(0\) | \(\frac{ 1}{ 3}\) | \(0\) | \(0\) | \(0\) | \(0\) |
\(0\) | \(\frac{ 2}{ 3}\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(0\) | \(\frac{ 4}{ 3}\) | \(3\) | \(1\) | \(1\) | \(1\) |
\(0\) | \(\frac{ 5}{ 3}\) | \(4\) | \(2\) | \(2\) | \(2\) |
12
New Number: 5.103 | AESZ: 354 | Superseeker: 25 17175 | Hash: 0d4263e8c85dceb5c51f8614f7c1bc79
Degree: 5
\(\theta^4-5 x\left(170\theta^4+160\theta^3+125\theta^2+45\theta+6\right)+3 5^{3} x^{2}\left(725\theta^4+1220\theta^3+1105\theta^2+460\theta+68\right)-3^{2} 5^{5} x^{3}\left(1421\theta^4+3186\theta^3+3053\theta^2+1272\theta+188\right)+2^{2} 3^{3} 5^{7} x^{4}(3\theta+1)(3\theta+2)(34\theta^2+61\theta+36)-2^{2} 3^{4} 5^{9} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 30, 3150, 462000, 78828750, ... --> OEIS Normalized instanton numbers (n0=1): 25, 2175/4, 17175, 351250, 23000351/5, ... ; Common denominator:...
\(-(2278125z^3-84375z^2+550z-1)(-1+150z)^2\)
\(0\) | ≈\(0.029311\) | ≈\(0.003863+0.000232I\) | ≈\(0.003863-0.000232I\) | \(\infty\) | \(\frac{ 1}{ 150}\) |
---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) | \(0\) |
\(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 2}{ 3}\) | \(1\) |
\(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 4}{ 3}\) | \(3\) |
\(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 5}{ 3}\) | \(4\) |
13
New Number: 5.126 | AESZ: | Superseeker: 110 729096 | Hash: 511069e41e6328e47a1ea996049096b4
Degree: 5
\(\theta^4-x\left(881\theta^4+1222\theta^3+878\theta^2+267\theta+30\right)+3 x^{2}\left(50601\theta^4+60024\theta^3+17189\theta^2+280\theta-340\right)-3^{2} 5 x^{3}\left(195867\theta^4+207846\theta^3+142719\theta^2+49068\theta+6316\right)+2^{2} 3^{4} 5^{2} x^{4}(3\theta+1)(3\theta+2)(1902\theta^2+1767\theta+386)+2^{2} 3^{6} 5^{4} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 30, 6210, 2004240, 789638850, ... --> OEIS Normalized instanton numbers (n0=1): 110, 12935/2, 729096, 247828991/2, 26419290920, ... ; Common denominator:...
\((675z-1)(27z-1)(z+1)(-1+90z)^2\)
\(0\) | \(\frac{ 1}{ 27}\) | \(\frac{ 1}{ 675}\) | \(\infty\) | \(\frac{ 1}{ 90}\) | \(-1\) |
---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) | \(0\) | \(0\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 2}{ 3}\) | \(1\) | \(1\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 4}{ 3}\) | \(3\) | \(1\) |
\(0\) | \(2\) | \(2\) | \(\frac{ 5}{ 3}\) | \(4\) | \(2\) |
14
New Number: 5.127 | AESZ: | Superseeker: 957/10 1581774/5 | Hash: 8b1c933faa73767af598d82d1e214624
Degree: 5
\(2^{2} 5^{2} \theta^4-2 3 5 x\left(1812\theta^4+3858\theta^3+2799\theta^2+870\theta+100\right)-3 x^{2}\left(293697\theta^4-124614\theta^3-930203\theta^2-562390\theta-95700\right)+3^{3} x^{3}\left(62631\theta^4+977400\theta^3+677140\theta^2+104550\theta-6300\right)+3^{5} 5 13 x^{4}(3\theta+1)(3\theta+2)(308\theta^2-16\theta-231)-3^{8} 13^{2} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 30, 5130, 1369200, 446603850, ... --> OEIS Normalized instanton numbers (n0=1): 957/10, 32493/10, 1581774/5, 423123141/10, 14142369903/2, ... ; Common denominator:...
\(-(6561z^3-4320z^2+567z-1)(10+117z)^2\)
\(0\) | ≈\(0.001788\) | ≈\(0.178154\) | \(\infty\) | ≈\(0.478494\) | \(-\frac{ 10}{ 117}\) |
---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) | \(0\) | \(0\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 2}{ 3}\) | \(1\) | \(1\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 4}{ 3}\) | \(1\) | \(3\) |
\(0\) | \(2\) | \(2\) | \(\frac{ 5}{ 3}\) | \(2\) | \(4\) |
15
New Number: 5.19 | AESZ: 180 | Superseeker: -624 -43406256 | Hash: c174fb2dfd87730e48b4ae8b57ac66df
Degree: 5
\(\theta^4-2^{4} 3 x\left(198\theta^4+72\theta^3+69\theta^2+33\theta+5\right)+2^{9} 3^{2} x^{2}\left(7614\theta^4+7128\theta^3+6813\theta^2+2529\theta+340\right)-2^{14} 3^{5} x^{3}\left(15714\theta^4+27216\theta^3+26343\theta^2+11151\theta+1685\right)+2^{19} 3^{9} x^{4}(3\theta+1)(3\theta+2)(576\theta^2+1008\theta+605)-2^{27} 3^{13} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 240, 173520, 170016000, 193451504400, ... --> OEIS Normalized instanton numbers (n0=1): -624, -137190, -43406256, -18281817141, -9083828410320, ... ; Common denominator:...
\(-(-1+864z)(2592z-1)^2(1728z-1)^2\)
\(0\) | \(\frac{ 1}{ 2592}\) | \(\frac{ 1}{ 1728}\) | \(\infty\) | \(\frac{ 1}{ 864}\) |
---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) | \(0\) |
\(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 2}{ 3}\) | \(1\) |
\(0\) | \(3\) | \(\frac{ 1}{ 2}\) | \(\frac{ 4}{ 3}\) | \(1\) |
\(0\) | \(4\) | \(1\) | \(\frac{ 5}{ 3}\) | \(2\) |