1
New Number: 2.63 | AESZ: 84 | Superseeker: -4 -44 | Hash: 908b978c0c447d3643c3018c40e7f5d1
Degree: 2
\(\theta^4-2^{2} x\left(32\theta^4+64\theta^3+63\theta^2+31\theta+6\right)+2^{8} x^{2}(4\theta+3)(\theta+1)^2(4\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 24, 936, 43008, 2145960, ... --> OEIS Normalized instanton numbers (n0=1): -4, -11, -44, -156, -288, ... ; Common denominator:...
\((64z-1)^2\)
| \(0\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|
| \(0\) | \(0\) | \(\frac{ 3}{ 4}\) |
| \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 5}{ 4}\) |
2
New Number: 2.65 | AESZ: 183 | Superseeker: -4 -556/9 | Hash: 04a3788c3f9ed53281ae824deb33d833
Degree: 2
\(\theta^4+2^{2} x(2\theta+1)^2(7\theta^2+7\theta+3)+2^{4} 3 x^{2}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -12, 324, -11280, 447300, ... --> OEIS Normalized instanton numbers (n0=1): -4, 8, -556/9, 624, -8928, ... ; Common denominator:...
\((48z+1)(64z+1)\)
| \(-\frac{ 1}{ 48}\) | \(-\frac{ 1}{ 64}\) | \(0\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(1\) | \(0\) | \(\frac{ 5}{ 4}\) |
| \(2\) | \(2\) | \(0\) | \(\frac{ 3}{ 2}\) |
3
New Number: 4.71 | AESZ: 353 | Superseeker: -4 -1580/9 | Hash: 33845d8200fe810109063e352fbfc8b1
Degree: 4
\(\theta^4-2^{2} x\left(52\theta^4+40\theta^3+37\theta^2+17\theta+3\right)+2^{4} x^{2}\left(960\theta^4+1536\theta^3+1512\theta^2+688\theta+123\right)-2^{8} x^{3}\left(1792\theta^4+4608\theta^3+5184\theta^2+2816\theta+597\right)+2^{14} x^{4}(4\theta+5)^2(4\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 324, 11856, 504900, ... --> OEIS Normalized instanton numbers (n0=1): -4, -24, -1580/9, -1580, -17120, ... ; Common denominator:...
\((16z-1)(64z-1)^3\)
| \(0\) | \(\frac{ 1}{ 64}\) | \(\frac{ 1}{ 16}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 4}\) |
| \(0\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 3}{ 4}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(1\) | \(\frac{ 5}{ 4}\) |
| \(0\) | \(2\) | \(2\) | \(\frac{ 5}{ 4}\) |
4
New Number: 5.99 | AESZ: 342 | Superseeker: -4 3856/9 | Hash: 009a00efdd065ef9ea58db999d777786
Degree: 5
\(\theta^4+2 x\left(50\theta^4+64\theta^3+52\theta^2+20\theta+3\right)+2^{2} 3 x^{2}\left(380\theta^4+992\theta^3+1166\theta^2+612\theta+117\right)+2^{2} 3^{2} x^{3}\left(2140\theta^4+5832\theta^3+5651\theta^2+2349\theta+360\right)+2^{4} 3^{6} x^{4}(2\theta+1)(20\theta^3+42\theta^2+35\theta+11)+2^{6} 3^{7} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -6, 54, 660, -69930, ... --> OEIS Normalized instanton numbers (n0=1): -4, -16, 3856/9, -3864, -20784, ... ; Common denominator:...
\((3888z^3+2592z^2+76z+1)(1+12z)^2\)
| ≈\(-0.636595\) | \(-\frac{ 1}{ 12}\) | ≈\(-0.015036-0.01334I\) | ≈\(-0.015036+0.01334I\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(1\) | \(3\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(2\) | \(4\) | \(2\) | \(2\) | \(0\) | \(\frac{ 3}{ 2}\) |
5
New Number: 11.1 | AESZ: | Superseeker: -4 550/3 | Hash: 9e36d74a520997fe52f0cbbfafae6aaf
Degree: 11
\(\theta^4+x\left(6+38\theta+96\theta^2+116\theta^3+91\theta^4\right)+x^{2}\left(1218+5950\theta+11076\theta^2+9388\theta^3+3649\theta^4\right)+x^{3}\left(32814+148542\theta+258070\theta^2+203832\theta^3+63585\theta^4\right)+2 x^{4}\left(244543\theta^4+938432\theta^3+1417427\theta^2+933049\theta+226317\right)+2^{2} x^{5}\left(374407\theta^4+1908784\theta^3+3407293\theta^2+2501538\theta+653454\right)+2^{2} 3 x^{6}\left(130530\theta^4+686256\theta^3+1382165\theta^2+1159645\theta+333030\right)+2^{3} x^{7}\left(276464\theta^4-92912\theta^3-3194335\theta^2-3755703\theta-1224450\right)+2^{4} x^{8}\left(341712\theta^4+1614816\theta^3+1576879\theta^2+219863\theta-145632\right)-2^{5} x^{9}\left(29968\theta^4+412128\theta^3+489227\theta^2+156573\theta-3258\right)+2^{8} 3 x^{10}\left(6368\theta^4+13600\theta^3+11014\theta^2+4187\theta+681\right)-2^{11} 3^{2} x^{11}(4\theta+3)(\theta+1)^2(4\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -6, 54, 12, -26010, ... --> OEIS Normalized instanton numbers (n0=1): -4, -11, 550/3, -2965/2, -3316, ... ; Common denominator:...
\(-(4z+1)(3z+1)(96z^3-1576z^2-62z-1)(1+11z-6z^2+16z^3)^2\)
| \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 4}\) | ≈\(-0.085955\) | ≈\(-0.019642-0.015722I\) | ≈\(-0.019642+0.015722I\) | \(0\) | ≈\(0.230478-0.820976I\) | ≈\(0.230478+0.820976I\) | ≈\(16.455951\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(2\) | \(2\) | \(0\) | \(4\) | \(4\) | \(2\) | \(\frac{ 5}{ 4}\) |
6
New Number: 6.17 | AESZ: | Superseeker: 2 224/9 | Hash: bbcabbebf6c04783d4ec5d0a5664f174
Degree: 6
\(\theta^4-x\left(14+73\theta+154\theta^2+162\theta^3+81\theta^4\right)+x^{2}\left(3256+11390\theta+15571\theta^2+9876\theta^3+2469\theta^4\right)-x^{3}\left(162708+457536\theta+476503\theta^2+215994\theta^3+35999\theta^4\right)+2 3 5 x^{4}\left(8837\theta^4+70696\theta^3+200535\theta^2+236572\theta+98316\right)-2^{2} 3^{2} 5^{2} 7 x^{5}(\theta+4)(\theta+1)(151\theta^2+755\theta+850)+2^{3} 3^{3} 5^{3} 7^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 14, 220, 3800, 70840, ... --> OEIS Normalized instanton numbers (n0=1): 2, -4, 224/9, -112, 4446/5, ... ; Common denominator:...
\((6z-1)(14z-1)(30z-1)(21z-1)(-1+5z)^2\)
| \(0\) | \(\frac{ 1}{ 30}\) | \(\frac{ 1}{ 21}\) | \(\frac{ 1}{ 14}\) | \(\frac{ 1}{ 6}\) | \(\frac{ 1}{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(4\) |
| \(0\) | \(2\) | \(2\) | \(2\) | \(2\) | \(1\) | \(5\) |
7
New Number: 6.18 | AESZ: | Superseeker: 3 64 | Hash: b127e33287ed87a366c178fc4678cdc4
Degree: 6
\(\theta^4-x\left(18+94\theta+199\theta^2+210\theta^3+105\theta^4\right)+2 x^{2}\left(2095\theta^4+8380\theta^3+13298\theta^2+9836\theta+2850\right)-2^{2} 3^{2} x^{3}\left(2310\theta^4+13860\theta^3+30739\theta^2+29847\theta+10763\right)+2^{3} 3^{3} x^{4}\left(4044\theta^4+32352\theta^3+91997\theta^2+109172\theta+45693\right)-2^{4} 3^{3} 5^{2} 7 x^{5}(\theta+4)(\theta+1)(61\theta^2+305\theta+345)+2^{5} 3^{5} 5^{2} 7^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 348, 7320, 168840, ... --> OEIS Normalized instanton numbers (n0=1): 3, -4, 64, -253, 4292, ... ; Common denominator:...
\((6z-1)(15z-1)(14z-1)(42z-1)(18z-1)(10z-1)\)
| \(0\) | \(\frac{ 1}{ 42}\) | \(\frac{ 1}{ 18}\) | \(\frac{ 1}{ 15}\) | \(\frac{ 1}{ 14}\) | \(\frac{ 1}{ 10}\) | \(\frac{ 1}{ 6}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(4\) |
| \(0\) | \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(5\) |
8
New Number: 7.3 | AESZ: | Superseeker: 3 64 | Hash: 8413250555ca536f1bdccfeed506ea4e
Degree: 7
\(\theta^4+x\theta(39\theta^3-30\theta^2-19\theta-4)+2 x^{2}\left(16\theta^4-1070\theta^3-1057\theta^2-676\theta-192\right)-2^{2} 3^{2} x^{3}(3\theta+2)(171\theta^3+566\theta^2+600\theta+316)-2^{5} 3^{3} x^{4}\left(384\theta^4+1542\theta^3+2635\theta^2+2173\theta+702\right)-2^{6} 3^{3} x^{5}(\theta+1)(1393\theta^3+5571\theta^2+8378\theta+4584)-2^{10} 3^{5} x^{6}(\theta+1)(\theta+2)(31\theta^2+105\theta+98)-2^{12} 3^{7} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 24, 192, 3384, ... --> OEIS Normalized instanton numbers (n0=1): 3, -4, 64, -253, 4292, ... ; Common denominator:...
\(-(8z+1)(24z-1)(3z+1)(4z+1)(12z+1)(1+18z)^2\)
| \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 12}\) | \(-\frac{ 1}{ 18}\) | \(0\) | \(\frac{ 1}{ 24}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(2\) |
| \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(3\) |
9
New Number: 8.42 | AESZ: | Superseeker: -4 140 | Hash: 7bc3855c04953ca11620400320722844
Degree: 8
\(\theta^4+2^{2} x\left(26\theta^4+34\theta^3+29\theta^2+12\theta+2\right)+2^{4} x^{2}\left(305\theta^4+662\theta^3+781\theta^2+436\theta+94\right)+2^{8} x^{3}\left(519\theta^4+1278\theta^3+1541\theta^2+933\theta+213\right)+2^{10} x^{4}\left(2266\theta^4+4988\theta^3+3535\theta^2+633\theta-162\right)+2^{14} 3 x^{5}\left(569\theta^4+1184\theta^3+740\theta^2-81\theta-128\right)+2^{18} 3 x^{6}\left(254\theta^4+354\theta^3+161\theta^2-33\theta-28\right)+2^{22} 3^{2} x^{7}\left(23\theta^4+34\theta^3+8\theta^2-9\theta-4\right)-2^{27} 3^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -8, 112, -1664, 23056, ... --> OEIS Normalized instanton numbers (n0=1): -4, 1/2, 140, 1025/2, -9196, ... ; Common denominator:...
\(-(32z+1)(1024z^3-896z^2-48z-1)(1+12z+192z^2)^2\)
| \(-\frac{ 1}{ 32}-\frac{ 1}{ 96}\sqrt{ 39}I\) | \(-\frac{ 1}{ 32}\) | \(-\frac{ 1}{ 32}+\frac{ 1}{ 96}\sqrt{ 39}I\) | ≈\(-0.025859-0.019623I\) | ≈\(-0.025859+0.019623I\) | \(0\) | ≈\(0.926719\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(1\) |
10
New Number: 6.35 | AESZ: | Superseeker: 2 224/9 | Hash: 31d226ff68f616edaab012f85462b8e9
Degree: 6
\(\theta^4-x\left(9+48\theta+104\theta^2+112\theta^3+41\theta^4\right)+2 x^{2}\left(167\theta^4+1358\theta^3+2593\theta^2+1990\theta+573\right)+2 x^{3}\left(1273\theta^4-822\theta^3-16239\theta^2-22188\theta-9009\right)-5 x^{4}\left(3923\theta^4+29740\theta^3+51878\theta^2+33360\theta+6534\right)-5^{2} x^{5}(\theta+1)(2929\theta^3+4467\theta^2-1969\theta-4047)+2^{2} 3^{2} 5^{4} x^{6}(\theta+2)(\theta+1)(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 9, 105, 1425, 21465, ... --> OEIS Normalized instanton numbers (n0=1): 2, -4, 224/9, -112, 4446/5, ... ; Common denominator:...
\(\)
No data for singularities