1
New Number: 5.110 | AESZ: 377 | Superseeker: 32/3 6752/3 | Hash: 4b8e1b4341fae957e1766a0071de5ba5
Degree: 5
\(3^{2} \theta^4-2^{3} 3 x\left(61\theta^4+74\theta^3+58\theta^2+21\theta+3\right)+2^{4} x^{2}\left(3883\theta^4+5356\theta^3+3451\theta^2+1278\theta+228\right)-2^{7} x^{3}\left(8067\theta^4+13410\theta^3+12875\theta^2+6336\theta+1236\right)+2^{14} x^{4}\left(413\theta^4+1069\theta^3+1206\theta^2+658\theta+140\right)-2^{19} 3 x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 264, 13760, 873640, ... --> OEIS Normalized instanton numbers (n0=1): 32/3, 731/6, 6752/3, 355219/6, 5936896/3, ... ; Common denominator:...
\(-(4z-1)(108z-1)(8z-1)(-3+64z)^2\)
| \(0\) | \(\frac{ 1}{ 108}\) | \(\frac{ 3}{ 64}\) | \(\frac{ 1}{ 8}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(2\) | \(4\) | \(2\) | \(2\) | \(\frac{ 4}{ 3}\) |
2
New Number: 5.24 | AESZ: 195 | Superseeker: 285/29 40626/29 | Hash: 49a600431b3e9aaa9d9d6947f8df7d2b
Degree: 5
\(29^{2} \theta^4-29 x\left(3026\theta^4+5848\theta^3+4577\theta^2+1653\theta+232\right)+x^{2}\left(5568+57768\theta+239159\theta^2+424220\theta^3+258647\theta^4\right)-x^{3}\left(76560+336864\theta+581647\theta^2+532614\theta^3+272743\theta^4\right)+2^{2} 17 x^{4}\left(1922\theta^4+6193\theta^3+8121\theta^2+4894\theta+1112\right)-2^{2} 3 17^{2} x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 264, 13040, 778840, ... --> OEIS Normalized instanton numbers (n0=1): 285/29, 2362/29, 40626/29, 997476/29, 30096841/29, ... ; Common denominator:...
\(-(27z^3-67z^2+102z-1)(-29+34z)^2\)
| \(0\) | ≈\(0.009868\) | \(\frac{ 29}{ 34}\) | ≈\(1.235807-1.492036I\) | ≈\(1.235807+1.492036I\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(2\) | \(4\) | \(2\) | \(2\) | \(\frac{ 4}{ 3}\) |
3
New Number: 14.1 | AESZ: | Superseeker: 0 0 | Hash: a8cf56492aecc07971e82c9104785180
Degree: 14
\(\theta^4-x\left(13\theta^4+14\theta^3+16\theta^2+9\theta+2\right)+x^{2}\left(33\theta^4-88\theta^3-265\theta^2-324\theta-148\right)+x^{3}\left(217\theta^4+2362\theta^3+6403\theta^2+8178\theta+4160\right)-2 x^{4}\left(677\theta^4+4134\theta^3+8089\theta^2+6210\theta+360\right)+2^{2} 3 x^{5}\left(151\theta^4-1266\theta^3-11610\theta^2-28955\theta-25110\right)+2^{2} x^{6}\left(1895\theta^4+37302\theta^3+176991\theta^2+355848\theta+268836\right)-2^{2} x^{7}\left(9635\theta^4+89170\theta^3+185885\theta^2-107394\theta-522464\right)+2^{3} x^{8}\left(5907\theta^4-10636\theta^3-416125\theta^2-1666326\theta-2051920\right)+2^{5} x^{9}\left(2947\theta^4+80284\theta^3+519934\theta^2+1328475\theta+1205150\right)-2^{6} x^{10}\left(6122\theta^4+84852\theta^3+397555\theta^2+722745\theta+356430\right)+2^{6} 3 x^{11}\left(2259\theta^4+13398\theta^3-46549\theta^2-456244\theta-796656\right)+2^{7} 3^{2} x^{12}(\theta+4)(371\theta^3+8580\theta^2+53325\theta+101564)-2^{10} 3^{3} x^{13}(\theta+4)(\theta+5)(51\theta^2+519\theta+1330)+2^{11} 3^{4} 5 x^{14}(\theta+4)(\theta+5)^2(\theta+6)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 2, 16, 48, 264, ... --> OEIS Normalized instanton numbers (n0=1): 0, 1/4, 0, -1/2, 0, ... ; Common denominator:...
\((z-1)(6z-1)(4z-1)(3z+1)(4z+1)(5z-1)(2z+1)^2(2z-1)^2(6z^2-2z+1)^2\)
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 4}\) | \(0\) | \(\frac{ 1}{ 6}-\frac{ 1}{ 6}\sqrt{ 5}I\) | \(\frac{ 1}{ 6}\) | \(\frac{ 1}{ 6}+\frac{ 1}{ 6}\sqrt{ 5}I\) | \(\frac{ 1}{ 5}\) | \(\frac{ 1}{ 4}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(4\) |
| \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(5\) |
| \(-1\) | \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(3\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(5\) |
| \(1\) | \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(4\) | \(2\) | \(2\) | \(1\) | \(2\) | \(6\) |
4
New Number: 8.49 | AESZ: | Superseeker: 56/3 17704/3 | Hash: 4fa01cbee2fc74e3a62e00386e6fa1c0
Degree: 8
\(3^{2} \theta^4-2^{2} 3 x\left(29\theta^4+178\theta^3+134\theta^2+45\theta+6\right)-2^{5} x^{2}\left(2233\theta^4+2536\theta^3+607\theta^2+132\theta+12\right)-2^{10} x^{3}\left(1274\theta^4+7425\theta^3+20002\theta^2+12717\theta+2670\right)+2^{13} x^{4}\left(2539\theta^4-36538\theta^3-52775\theta^2-31122\theta-6192\right)+2^{20} x^{5}\left(1617\theta^4+9771\theta^3+4484\theta^2-674\theta-556\right)+2^{25} x^{6}\left(1135\theta^4+4272\theta^3+3439\theta^2+858\theta+16\right)-2^{31} 3 x^{7}(2\theta+1)(110\theta^3+225\theta^2+184\theta+57)+2^{37} 3^{2} x^{8}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 264, 16640, 1130920, ... --> OEIS Normalized instanton numbers (n0=1): 56/3, -83/6, 17704/3, -25024/3, 13408832/3, ... ; Common denominator:...
\((4z-1)(131072z^3+2048z^2+88z-1)(48z+1)^2(64z-3)^2\)
| \(-\frac{ 1}{ 48}\) | ≈\(-0.01214-0.027095I\) | ≈\(-0.01214+0.027095I\) | \(0\) | ≈\(0.008655\) | \(\frac{ 3}{ 64}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |