31
New Number: 6.40 | AESZ: | Superseeker: 24586 329889747608 | Hash: 36fe35d15f62636c9a59974b02c3c153
Degree: 6
\(\theta^4+2 x\left(31252\theta^4-47788\theta^3-30351\theta^2-6457\theta-777\right)+2^{2} x^{2}\left(141990396\theta^4-851496456\theta^3+348245465\theta^2+120244516\theta+24723417\right)-2^{4} 7 x^{3}\left(114890001328\theta^4-55808058864\theta^3-39178895096\theta^2-22533986391\theta-2840254281\right)+2^{6} 7^{2} x^{4}\left(12756705884284\theta^4+28777665785840\theta^3+28025191186334\theta^2+13259372733985\theta+2453710035513\right)+2^{8} 3^{4} 7^{3} 13 101 x^{5}(\theta+1)(6017971352\theta^3+13862309856\theta^2+7944674578\theta+1672187649)-2^{10} 3^{10} 5^{2} 7^{5} 13^{2} 37^{2} 101^{2} x^{6}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 1554, 4332150, 14528884020, 53714646216630, ... --> OEIS Normalized instanton numbers (n0=1): 24586, -65016808, 329889747608, -2211583844012928, 17318548806048850836, ... ; Common denominator:...
\(-(2916z-1)(5476z-1)(2268z+1)(4900z-1)(1+36764z)^2\)
| \(-\frac{ 1}{ 2268}\) | \(-\frac{ 1}{ 36764}\) | \(0\) | \(\frac{ 1}{ 5476}\) | \(\frac{ 1}{ 4900}\) | \(\frac{ 1}{ 2916}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 5}{ 2}\) |
32
New Number: 6.3 | AESZ: | Superseeker: 178/7 129516/7 | Hash: ec9e21dc2ccd3b4b4156ae1438454b96
Degree: 6
\(7^{2} \theta^4-2 7 x\left(1488\theta^4+1452\theta^3+1125\theta^2+399\theta+56\right)+2^{2} x^{2}\left(766392\theta^4+1184952\theta^3+1010797\theta^2+454076\theta+83776\right)-2^{4} x^{3}\left(12943616\theta^4+28354200\theta^3+30710572\theta^2+16054731\theta+3215254\right)+2^{6} x^{4}\left(105973188\theta^4+333359304\theta^3+436182381\theta^2+261265857\theta+57189166\right)-2^{11} 127 x^{5}(\theta+1)(390972\theta^3+1350660\theta^2+1486781\theta+460439)+2^{14} 23^{2} 127^{2} x^{6}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 864, 80800, 9624160, ... --> OEIS Normalized instanton numbers (n0=1): 178/7, 3375/7, 129516/7, 6515900/7, 409239710/7, ... ; Common denominator:...
\((1-248z+8464z^2)(508z-7)^2(16z-1)^2\)
| \(0\) | \(\frac{ 31}{ 2116}-\frac{ 3}{ 529}\sqrt{ 3}\) | \(\frac{ 7}{ 508}\) | \(\frac{ 31}{ 2116}+\frac{ 3}{ 529}\sqrt{ 3}\) | \(\frac{ 1}{ 16}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 3}\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(1\) | \(\frac{ 2}{ 3}\) | \(2\) |
| \(0\) | \(2\) | \(4\) | \(2\) | \(1\) | \(\frac{ 5}{ 2}\) |
33
New Number: 6.4 | AESZ: | Superseeker: 370/19 140636/19 | Hash: 0f3ddf420018e2870561a3e9fd2551cc
Degree: 6
\(19^{2} \theta^4-19 x\left(4333\theta^4+6212\theta^3+4778\theta^2+1672\theta+228\right)+x^{2}\left(4307495\theta^4+7600484\theta^3+6216406\theta^2+2802424\theta+530556\right)-x^{3}\left(93729369\theta^4+213316800\theta^3+236037196\theta^2+125748612\theta+25260804\right)+2^{2} x^{4}\left(240813800\theta^4+778529200\theta^3+1041447759\theta^2+631802809\theta+138510993\right)-2^{2} 409 x^{5}(\theta+1)(2851324\theta^3+10035516\theta^2+11221241\theta+3481470)+2^{2} 3^{2} 19^{2} 409^{2} x^{6}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 588, 46200, 4446540, ... --> OEIS Normalized instanton numbers (n0=1): 370/19, 276, 140636/19, 5568700/19, 277119292/19, ... ; Common denominator:...
\((9z-1)(5776z^3-1920z^2+176z-1)(-19+409z)^2\)
| \(0\) | ≈\(0.006077\) | \(\frac{ 19}{ 409}\) | \(\frac{ 1}{ 9}\) | ≈\(0.163166-0.043179I\) | ≈\(0.163166+0.043179I\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(0\) | \(2\) | \(4\) | \(2\) | \(2\) | \(2\) | \(\frac{ 5}{ 2}\) |
34
New Number: 6.5 | AESZ: | Superseeker: -11 -3422/3 | Hash: 6a4aeb5833b7673c962d5598842d3f2c
Degree: 6
\(\theta^4-x\left(12+64\theta+125\theta^2+122\theta^3+61\theta^4\right)-2^{3} x^{2}\left(193\theta^4+772\theta^3+1033\theta^2+522\theta+72\right)+2^{9} 3 x^{3}\left(146\theta^4+876\theta^3+1838\theta^2+1572\theta+405\right)-2^{12} 3^{2} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)+2^{16} 3^{3} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2-2^{19} 3^{4} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 324, 5760, 215460, ... --> OEIS Normalized instanton numbers (n0=1): -11, 68, -3422/3, 30735, -1014993, ... ; Common denominator:...
\(-(24z-1)(27648z^3-1728z^2+27z+1)(-1+32z)^2\)
| ≈\(-0.016119\) | \(0\) | \(\frac{ 1}{ 32}\) | ≈\(0.03931-0.026431I\) | ≈\(0.03931+0.026431I\) | \(\frac{ 1}{ 24}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(2\) | \(0\) | \(1\) | \(2\) | \(2\) | \(2\) | \(\frac{ 11}{ 2}\) |
35
New Number: 6.6 | AESZ: | Superseeker: 25 17452 | Hash: e97e9b0e87960fe4cffbb22a5e935b4a
Degree: 6
\(\theta^4-x\left(12+100\theta+305\theta^2+410\theta^3+205\theta^4\right)-2^{5} x^{2}\left(127\theta^4+508\theta^3+742\theta^2+468\theta+99\right)-2^{2} 3 x^{3}\left(2588\theta^4+15528\theta^3+32639\theta^2+28041\theta+7290\right)-2^{6} 3^{2} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)-2^{7} 3^{3} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2-2^{7} 3^{4} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 972, 106200, 14027580, ... --> OEIS Normalized instanton numbers (n0=1): 25, 446, 17452, 958347, 65098152, ... ; Common denominator:...
\(-(3z+1)(3456z^3+1728z^2+216z-1)(4z+1)^2\)
| \(-\frac{ 1}{ 3}\) | ≈\(-0.252234-0.033647I\) | ≈\(-0.252234+0.033647I\) | \(-\frac{ 1}{ 4}\) | \(0\) | \(\frac{ 1}{ 12}2^(\frac{ 1}{ 3})+\frac{ 1}{ 24}2^(\frac{ 2}{ 3})-\frac{ 1}{ 6}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(2\) | \(2\) | \(2\) | \(1\) | \(0\) | \(2\) | \(\frac{ 11}{ 2}\) |
36
New Number: 6.7 | AESZ: | Superseeker: -9 217/3 | Hash: 9492f991c909a6774f5546668ff53b6a
Degree: 6
\(\theta^4-3 x\left(42\theta^4+84\theta^3+77\theta^2+35\theta+6\right)+3^{3} x^{2}\left(291\theta^4+1164\theta^3+1747\theta^2+1166\theta+264\right)-2^{2} 3^{5} x^{3}\left(360\theta^4+2160\theta^3+4553\theta^2+3939\theta+1035\right)+2^{3} 3^{8} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)-2^{4} 3^{11} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2+2^{4} 3^{14} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 378, 8820, 266490, ... --> OEIS Normalized instanton numbers (n0=1): -9, 18, 217/3, -9, -146079, ... ; Common denominator:...
\((27z-1)(34992z^3-1944z^2+27z-1)(-1+36z)^2\)
| \(0\) | ≈\(0.002095-0.023494I\) | ≈\(0.002095+0.023494I\) | \(\frac{ 1}{ 36}\) | \(\frac{ 1}{ 27}\) | ≈\(0.051365\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(0\) | \(2\) | \(2\) | \(1\) | \(2\) | \(2\) | \(\frac{ 11}{ 2}\) |
37
New Number: 6.8 | AESZ: | Superseeker: 567/13 512341/13 | Hash: 00104510dfaa4ae75940f08df0a52bf5
Degree: 6
\(13^{2} \theta^4-13 x\left(5041\theta^4+7634\theta^3+5767\theta^2+1950\theta+260\right)+2^{3} x^{2}\left(744635\theta^4+1560842\theta^3+1510101\theta^2+768170\theta+156078\right)-2^{6} 3 x^{3}\left(1232985\theta^4+3409302\theta^3+4189688\theta^2+2419209\theta+518414\right)+2^{9} x^{4}\left(9225025\theta^4+33675338\theta^3+49289090\theta^2+31849807\theta+7296732\right)-2^{12} 3 17 x^{5}(\theta+1)(222704\theta^3+833160\theta^2+989659\theta+317310)+2^{15} 3^{2} 17^{2} 23^{2} x^{6}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 20, 1524, 196400, 31587220, ... --> OEIS Normalized instanton numbers (n0=1): 567/13, 11392/13, 512341/13, 34191454/13, 2850663840/13, ... ; Common denominator:...
\((1-293z+4232z^2)(408z-13)^2(16z-1)^2\)
| \(0\) | \(\frac{ 293}{ 8464}-\frac{ 41}{ 8464}\sqrt{ 41}\) | \(\frac{ 13}{ 408}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 293}{ 8464}+\frac{ 41}{ 8464}\sqrt{ 41}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(2\) |
| \(0\) | \(2\) | \(4\) | \(1\) | \(2\) | \(\frac{ 5}{ 2}\) |
38
New Number: 6.9 | AESZ: | Superseeker: 31/81 29/9 | Hash: 98af5121f39c27098356e3ade277f975
Degree: 6
\(3^{8} \theta^4-3^{4} x\left(1234\theta^4+2168\theta^3+1975\theta^2+891\theta+162\right)-x^{2}\left(428004+1521180\theta+2033921\theta^2+1177556\theta^3+205589\theta^4\right)+x^{3}\left(2310517\theta^4+12882402\theta^3+26939429\theta^2+25052328\theta+8683524\right)-2^{2} 5^{2} x^{4}\left(51526\theta^4+332687\theta^3+804453\theta^2+849398\theta+325796\right)+2^{2} 5^{4} x^{5}(\theta+1)(1593\theta^3+8667\theta^2+15104\theta+8516)-2^{4} 5^{6} x^{6}(\theta+2)(\theta+1)(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 2, 14, 104, 1030, ... --> OEIS Normalized instanton numbers (n0=1): 31/81, 40/27, 29/9, 1532/81, 6551/81, ... ; Common denominator:...
\(-(16z-1)(25z^3-17z^2+2z+1)(-81+50z)^2\)
| ≈\(-0.17455\) | \(0\) | \(\frac{ 1}{ 16}\) | ≈\(0.427275-0.215865I\) | ≈\(0.427275+0.215865I\) | \(\frac{ 81}{ 50}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(2\) |
39
New Number: 6.13 | AESZ: | Superseeker: 0 0 | Hash: b7b28238d79425febad0c26d36cce7ef
Degree: 6
\(3 \theta^4-2 3 5^{2} x\left(8\theta^4+10\theta^3+10\theta^2+5\theta+1\right)+2^{2} 3 5 x^{2}\left(3129\theta^4+7266\theta^3+9285\theta^2+5913\theta+1490\right)-2^{3} 3 5^{3} x^{3}\left(4774\theta^4+15120\theta^3+22026\theta^2+15303\theta+4073\right)+2^{4} 3 5^{5} x^{4}\left(3552\theta^4+13296\theta^3+20195\theta^2+13733\theta+3492\right)-2^{6} 3 5^{7} x^{5}(\theta+1)^2(524\theta^2+1096\theta+611)+2^{10} 5^{9} x^{6}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 50, 3450, 267500, 22029250, ... --> OEIS Normalized instanton numbers (n0=1): 0, 165/4, 0, -44335/8, 0, ... ; Common denominator:...
\(\)
No data for singularities
40
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