1
New Number: 5.55 | AESZ: 261 | Superseeker: -76/5 -24836/5 | Hash: adadb5e720011482371f48cfa73dab99
Degree: 5
\(5^{2} \theta^4+2^{2} 5 x\left(292\theta^4+368\theta^3+289\theta^2+105\theta+15\right)+2^{4} x^{2}\left(24736\theta^4+43648\theta^3+38936\theta^2+18980\theta+3735\right)+2^{9} 3^{2} x^{3}\left(2512\theta^4+5760\theta^3+6328\theta^2+3330\theta+655\right)+2^{12} 3^{4} x^{4}(2\theta+1)(232\theta^3+588\theta^2+590\theta+207)+2^{18} 3^{6} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -12, 492, -32880, 2743020, ... --> OEIS Normalized instanton numbers (n0=1): -76/5, 1103/5, -24836/5, 847456/5, -36542448/5, ... ; Common denominator:...
\((1+144z)(16z+1)^2(144z+5)^2\)
\(-\frac{ 1}{ 16}\) | \(-\frac{ 5}{ 144}\) | \(-\frac{ 1}{ 144}\) | \(0\) | \(\infty\) |
---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) |
\(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(0\) | \(1\) |
\(1\) | \(4\) | \(2\) | \(0\) | \(\frac{ 3}{ 2}\) |
2
New Number: 5.62 | AESZ: 270 | Superseeker: -76/5 -2100 | Hash: 256e3b3a92e3fd332be8b01f71853ea4
Degree: 5
\(5^{2} \theta^4-2^{2} 5 x\left(48\theta^4+192\theta^3+251\theta^2+155\theta+35\right)-2^{4} x^{2}\left(8704\theta^4+28672\theta^3+43664\theta^2+31760\theta+9265\right)+2^{11} x^{3}\left(1792\theta^4+15360\theta^3+36248\theta^2+33240\theta+10795\right)+2^{16} x^{4}\left(2304\theta^4+12288\theta^3+20816\theta^2+14672\theta+3719\right)+2^{30} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 28, 1324, 63856, 3489004, ... --> OEIS Normalized instanton numbers (n0=1): -76/5, 367/5, -2100, 43436, -6582256/5, ... ; Common denominator:...
\((1+64z)(64z+5)^2(64z-1)^2\)
\(-\frac{ 5}{ 64}\) | \(-\frac{ 1}{ 64}\) | \(0\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(1\) | \(1\) | \(0\) | \(-\frac{ 1}{ 4}\) | \(1\) |
\(3\) | \(1\) | \(0\) | \(1\) | \(1\) |
\(4\) | \(2\) | \(0\) | \(\frac{ 5}{ 4}\) | \(1\) |
3
New Number: 12.13 | AESZ: | Superseeker: 92/5 -76/5 | Hash: dba247c75acfa39c7b95fa5054ec0315
Degree: 12
\(5^{2} \theta^4-2^{2} 5 x\left(204\theta^4+456\theta^3+413\theta^2+185\theta+35\right)+2^{4} x^{2}\left(15584\theta^4+68672\theta^3+112204\theta^2+80560\theta+23355\right)-2^{8} x^{3}\left(31248\theta^4+175968\theta^3+412240\theta^2+410040\theta+153195\right)+2^{12} x^{4}\left(51632\theta^4+209728\theta^3+475320\theta^2+630640\theta+291767\right)-2^{17} x^{5}\left(49392\theta^4+140352\theta^3+11864\theta^2-35120\theta-12789\right)+2^{22} 3 x^{6}\left(12592\theta^4+46080\theta^3+11800\theta^2-52224\theta-39545\right)-2^{27} x^{7}\left(20208\theta^4+72192\theta^3+95128\theta^2+2176\theta-35669\right)+2^{32} x^{8}\left(10672\theta^4+18112\theta^3+35960\theta^2+24560\theta+3975\right)-2^{37} x^{9}\left(5904\theta^4+9216\theta^3+9640\theta^2+6720\theta+2709\right)+2^{42} x^{10}\left(2224\theta^4+6464\theta^3+8328\theta^2+5360\theta+1507\right)-2^{47} x^{11}\left(432\theta^4+1920\theta^3+3400\theta^2+2816\theta+915\right)+2^{53} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 28, 876, 30512, 1161964, ... --> OEIS Normalized instanton numbers (n0=1): 92/5, -342/5, -76/5, 75394/5, -2156752/5, ... ; Common denominator:...
\((64z-1)(32z-1)(256z^2-48z+1)(16z-1)^2(32768z^3-1024z^2-32z-5)^2\)
≈\(-0.020941-0.040594I\) | ≈\(-0.020941+0.040594I\) | \(0\) | \(\frac{ 1}{ 64}\) | \(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 32}\) | \(\frac{ 1}{ 16}\) | ≈\(0.073133\) | \(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\infty\) |
---|---|---|---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
\(3\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) | \(\frac{ 3}{ 2}\) |
\(4\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(1\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
4
New Number: 14.8 | AESZ: | Superseeker: 92/5 -76/5 | Hash: a787adbb87527c14af9a5f2508991317
Degree: 14
\(5^{2} \theta^4-2^{2} 5 x\left(244\theta^4+496\theta^3+473\theta^2+225\theta+45\right)+2^{4} x^{2}\left(24144\theta^4+95872\theta^3+155244\theta^2+117660\theta+36835\right)-2^{9} x^{3}\left(33248\theta^4+180880\theta^3+407234\theta^2+416430\theta+168275\right)+2^{14} x^{4}\left(32428\theta^4+181000\theta^3+474021\theta^2+605903\theta+294817\right)-2^{19} x^{5}\left(29162\theta^4+130236\theta^3+270865\theta^2+378135\theta+208235\right)+2^{24} x^{6}\left(25019\theta^4+101558\theta^3+110864\theta^2+69739\theta+20552\right)-2^{29} x^{7}\left(17583\theta^4+76998\theta^3+91248\theta^2+4717\theta-39868\right)+2^{34} x^{8}\left(10081\theta^4+40990\theta^3+72600\theta^2+35261\theta-9816\right)-2^{39} x^{9}\left(5407\theta^4+16538\theta^3+33406\theta^2+27573\theta+6100\right)+2^{44} x^{10}\left(2699\theta^4+7862\theta^3+13380\theta^2+11845\theta+4325\right)-2^{49} x^{11}\left(1033\theta^4+3966\theta^3+6998\theta^2+6213\theta+2329\right)+2^{54} x^{12}\left(255\theta^4+1318\theta^3+2815\theta^2+2864\theta+1159\right)-2^{59} x^{13}\left(35\theta^4+230\theta^3+589\theta^2+692\theta+313\right)+2^{65} x^{14}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 36, 1196, 41488, 1543916, ... --> OEIS Normalized instanton numbers (n0=1): 92/5, -342/5, -76/5, 75394/5, -2156752/5, ... ; Common denominator:...
\((64z-1)(32z-1)(256z^2-48z+1)(32768z^3-1024z^2-5-32z)^2(16z-1)^4\)
≈\(-0.020941-0.040594I\) | ≈\(-0.020941+0.040594I\) | \(0\) | \(\frac{ 1}{ 64}\) | \(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 32}\) | \(\frac{ 1}{ 16}\) | ≈\(0.073133\) | \(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\infty\) |
---|---|---|---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(2\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(-\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(2\) |
\(3\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(2\) |
\(4\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 1}{ 2}\) | \(4\) | \(2\) | \(2\) |