1
New Number: 11.8 | AESZ: | Superseeker: 6/17 688/17 | Hash: a0a3e346d09b91b8ad96e54854c136ad
Degree: 11
\(17^{2} \theta^4-2 3 17 x\theta^2(117\theta^2+2\theta+1)+2^{2} x^{2}\left(8475\theta^4-64176\theta^3-97010\theta^2-63580\theta-16184\right)+2^{2} x^{3}\left(717094\theta^4+1400796\theta^3+1493367\theta^2+893571\theta+254082\right)-2^{4} x^{4}\left(464294\theta^4-1133264\theta^3-1648391\theta^2-1200310\theta-375336\right)-2^{4} x^{5}\left(18282700\theta^4+46995928\theta^3+83098711\theta^2+73517673\theta+25685438\right)-2^{6} 3 x^{6}\left(2709886\theta^4+7353008\theta^3+18175093\theta^2+18787708\theta+5966228\right)+2^{6} x^{7}\left(154368940\theta^4+947965400\theta^3+2363187035\theta^2+2646307981\theta+1071488886\right)+2^{8} x^{8}(\theta+1)(119648213\theta^3+399067803\theta^2+77665606\theta-498465144)-2^{8} 3 x^{9}(\theta+1)(\theta+2)(120410834\theta^2+865960638\theta+1188072247)-2^{10} 3^{2} 107 x^{10}(\theta+3)(\theta+2)(\theta+1)(218683\theta-39394)+2^{11} 3^{3} 5 107^{2} 137 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 14, 72, 1554, ... --> OEIS Normalized instanton numbers (n0=1): 6/17, 83/17, 688/17, 7350/17, 5150, ... ; Common denominator:...
\((10z+1)(6z-1)(1096z^3+228z^2+14z-1)(2z-1)^2(1284z^2+232z-17)^2\)
| \(-\frac{ 29}{ 321}-\frac{ 1}{ 642}\sqrt{ 8821}\) | ≈\(-0.124082-0.085658I\) | ≈\(-0.124082+0.085658I\) | \(-\frac{ 1}{ 10}\) | \(0\) | ≈\(0.040135\) | \(-\frac{ 29}{ 321}+\frac{ 1}{ 642}\sqrt{ 8821}\) | \(\frac{ 1}{ 6}\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(0\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) | \(4\) |
2
New Number: 6.27 | AESZ: | Superseeker: 6/17 33/17 | Hash: af5aea32756746d4fc4931e4da73756b
Degree: 6
\(17^{6} \theta^4-17^{5} x\left(427\theta^4+854\theta^3+814\theta^2+387\theta+74\right)+17^{4} x^{2}\left(47239\theta^4+188956\theta^3+300763\theta^2+223614\theta+64536\right)-2 3 17^{3} x^{3}\left(237751\theta^4+1426506\theta^3+3169919\theta^2+3090480\theta+1104868\right)-2^{2} 3^{2} 17^{2} x^{4}\left(1549605\theta^4+12396840\theta^3+35038211\theta^2+40978124\theta+16802716\right)+2^{3} 3^{3} 7 17 139 x^{5}(\theta+4)(\theta+1)(3737\theta^2+18685\theta+21310)-2^{5} 3^{4} 7^{2} 139^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 74/17, 7788/289, 1036400/4913, 164905648/83521, ... --> OEIS Normalized instanton numbers (n0=1): 6/17, 25/34, 33/17, 157/17, 577/17, ... ; Common denominator:...
\(-(28z+17)(278z-17)(8757z^2-2805z+289)(6z-17)^2\)
| \(-\frac{ 17}{ 28}\) | \(0\) | \(\frac{ 17}{ 278}\) | \(\frac{ 935}{ 5838}-\frac{ 289}{ 5838}\sqrt{ 3}I\) | \(\frac{ 935}{ 5838}+\frac{ 289}{ 5838}\sqrt{ 3}I\) | \(\frac{ 17}{ 6}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(4\) |
| \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(1\) | \(5\) |
3
New Number: 8.68 | AESZ: | Superseeker: 6/17 33/17 | Hash: 0c0662f5b46ac6cb0bd298a63cf364c7
Degree: 8
\(17^{2} \theta^4+17 x\theta(165\theta^3-114\theta^2-74\theta-17)-x^{2}\left(20619\theta^4+122880\theta^3+175353\theta^2+126480\theta+36992\right)-2 x^{3}\left(201857\theta^4+853944\theta^3+1437673\theta^2+1174122\theta+375972\right)-2^{2} x^{4}\left(571275\theta^4+2711616\theta^3+5301571\theta^2+4856674\theta+1694372\right)-2^{3} 3 x^{5}(\theta+1)(295815\theta^3+1523993\theta^2+2924668\theta+1983212)-2^{5} x^{6}(\theta+1)(\theta+2)(558823\theta^2+2951265\theta+4136951)-2^{7} 3 37 x^{7}(\theta+3)(\theta+2)(\theta+1)(2797\theta+9878)-2^{9} 3^{2} 7 37^{2} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 8, 24, 288, ... --> OEIS Normalized instanton numbers (n0=1): 6/17, 25/34, 33/17, 157/17, 577/17, ... ; Common denominator:...
\(-(12z-1)(6z+1)(7z^2-z+1)(4z+1)^2(74z+17)^2\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 17}{ 74}\) | \(-\frac{ 1}{ 6}\) | \(0\) | \(\frac{ 1}{ 14}-\frac{ 3}{ 14}\sqrt{ 3}I\) | \(\frac{ 1}{ 14}+\frac{ 3}{ 14}\sqrt{ 3}I\) | \(\frac{ 1}{ 12}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) |
| \(1\) | \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) |
4
New Number: 9.8 | AESZ: | Superseeker: 6/17 688/17 | Hash: 0574d9effd306eb6c9288752b7670904
Degree: 9
\(17^{2} \theta^4-2 17 x\left(164\theta^4-164\theta^3-167\theta^2-85\theta-17\right)-2^{2} x^{2}\left(35300\theta^4+95864\theta^3+121575\theta^2+70856\theta+16235\right)+2^{2} x^{3}\left(427984\theta^4-277824\theta^3-1460293\theta^2-1490475\theta-492694\right)+2^{4} x^{4}\left(2088512\theta^4+6692704\theta^3+7319011\theta^2+3820745\theta+794302\right)-2^{6} x^{5}\left(1379872\theta^4-6413120\theta^3-11843583\theta^2-9110135\theta-2589134\right)-2^{8} x^{6}\left(13237904\theta^4+37140384\theta^3+64254239\theta^2+57084594\theta+19379105\right)-2^{10} 3^{2} 5 x^{7}\left(255072\theta^4+803200\theta^3+1114259\theta^2+709496\theta+167515\right)+2^{12} 3^{3} 5^{2} 7 x^{8}(2224\theta^2+11008\theta+12225)(\theta+1)^2+2^{18} 3^{3} 5^{4} 7^{2} x^{9}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -2, 18, -20, 1330, ... --> OEIS Normalized instanton numbers (n0=1): 6/17, 83/17, 688/17, 7350/17, 5150, ... ; Common denominator:...
\((4z-1)(12z+1)(1600z^3+272z^2+8z-1)(-17+164z+1680z^2)^2\)
| \(-\frac{ 41}{ 840}-\frac{ 1}{ 840}\sqrt{ 8821}\) | ≈\(-0.106819-0.053966I\) | ≈\(-0.106819+0.053966I\) | \(-\frac{ 1}{ 12}\) | \(0\) | ≈\(0.043637\) | \(-\frac{ 41}{ 840}+\frac{ 1}{ 840}\sqrt{ 8821}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(2\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(2\) |