1
New Number: 4.32 | AESZ: 356 | Superseeker: -14 -196 | Hash: e73c971c3ed3a4fd581234510642c285
Degree: 4
\(\theta^4-2 x\left(236\theta^4+472\theta^3+577\theta^2+341\theta+78\right)+2^{2} x^{2}\left(20836\theta^4+83344\theta^3+150531\theta^2+134374\theta+48664\right)-2^{6} 3 x^{3}\left(33984\theta^4+203904\theta^3+487828\theta^2+545916\theta+237757\right)+2^{10} 3^{2} x^{4}(12\theta+19)(12\theta+23)(12\theta+25)(12\theta+29)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 156, 21062, 2714208, 342489420, ... --> OEIS Normalized instanton numbers (n0=1): -14, -42, -196, -1218, -208446/5, ... ; Common denominator:...
\((128z-1)^2(108z-1)^2\)
| \(0\) | \(\frac{ 1}{ 128}\) | \(\frac{ 1}{ 108}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 19}{ 12}\) |
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 23}{ 12}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 25}{ 12}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 29}{ 12}\) |
2
New Number: 7.8 | AESZ: | Superseeker: -1/3 -5/3 | Hash: d5b8cfd5049e5d8670dac5bb5499d46a
Degree: 7
\(3^{2} \theta^4-3 x\left(272\theta^4+340\theta^3+347\theta^2+177\theta+36\right)+x^{2}\left(31273\theta^4+76540\theta^3+103783\theta^2+71112\theta+19728\right)-2 x^{3}\left(328219\theta^4+1181160\theta^3+1977957\theta^2+1620036\theta+522288\right)+2^{2} x^{4}\left(2036999\theta^4+9602752\theta^3+19022113\theta^2+17726192\theta+6309408\right)-2^{3} 17 x^{5}(\theta+1)(439669\theta^3+2114103\theta^2+3708554\theta+2306280)+2^{6} 3^{3} 17^{2} x^{6}(\theta+1)(\theta+2)(481\theta^2+1875\theta+1962)-2^{10} 3^{4} 17^{3} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 156, 2136, 30348, ... --> OEIS Normalized instanton numbers (n0=1): -1/3, 11/12, -5/3, 19/3, -29, ... ; Common denominator:...
\(-(17z-1)(9z-1)(8z-1)(18z-1)(16z-1)(-3+34z)^2\)
| \(0\) | \(\frac{ 1}{ 18}\) | \(\frac{ 1}{ 17}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 3}{ 34}\) | \(\frac{ 1}{ 9}\) | \(\frac{ 1}{ 8}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) | \(1\) | \(2\) |
| \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(2\) | \(2\) | \(3\) |
3
New Number: 13.17 | AESZ: | Superseeker: 51/7 4071/7 | Hash: 1eb2bb810b4c7f191a26886aee350e18
Degree: 13
\(5^{2} 7^{2} \theta^4-3 5^{2} 7 x\left(169\theta^4+342\theta^3+269\theta^2+98\theta+14\right)-2 5 x^{2}\left(29068\theta^4+101254\theta^3+142979\theta^2+94430\theta+24780\right)-5 x^{3}\left(72227\theta^4+286050\theta^3+501033\theta^2+425670\theta+139608\right)+2 x^{4}\left(286748\theta^4-779402\theta^3-3422963\theta^2-2684470\theta-681300\right)-x^{5}\left(7490076+19892278\theta+15897011\theta^2-984006\theta^3-2224575\theta^4\right)+2 x^{6}\left(1109623\theta^4+1537878\theta^3-5243929\theta^2-10596978\theta-5189688\right)-2^{2} x^{7}\left(237446\theta^4-1827746\theta^3+1743127\theta^2+3795959\theta+1620252\right)-2^{3} 3^{2} x^{8}\left(58344\theta^4-162618\theta^3-74839\theta^2+120781\theta+86822\right)-2^{2} 3^{2} x^{9}\left(77741\theta^4-159874\theta^3-463443\theta^2-327512\theta-56132\right)+2^{3} 3^{3} x^{10}\left(721\theta^4+12222\theta^3+39317\theta^2+44772\theta+17268\right)-2^{5} 3^{3} x^{11}(\theta+1)(657\theta^3+1363\theta^2+689\theta-222)-2^{5} 3^{3} 13 x^{12}(\theta+2)(\theta+1)(115\theta^2+339\theta+270)-2^{6} 3^{3} 13^{2} x^{13}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 156, 5796, 259296, ... --> OEIS Normalized instanton numbers (n0=1): 51/7, 1552/35, 4071/7, 378248/35, 1721920/7, ... ; Common denominator:...
\(\)
No data for singularities