1
New Number: 12.10 | AESZ: | Superseeker: 224 4999008 | Hash: d0e84951fc25cf38a32ec7fba5893d59
Degree: 12
\(\theta^4+2^{4} x\left(160\theta^4+32\theta^3+56\theta^2+40\theta+9\right)+2^{13} x^{2}\left(328\theta^4+304\theta^3+442\theta^2+240\theta+57\right)+2^{22} x^{3}\left(416\theta^4+696\theta^3+939\theta^2+738\theta+225\right)+2^{28} 3 x^{4}\left(1120\theta^4+1856\theta^3+3196\theta^2+2832\theta+959\right)+2^{39} 3^{2} x^{5}\left(76\theta^4+128\theta^3+168\theta^2+168\theta+61\right)+2^{45} 3 x^{6}\left(1232\theta^4+2160\theta^3+2420\theta^2+1344\theta+273\right)+2^{54} 3 x^{7}\left(696\theta^4+1272\theta^3+1781\theta^2+554\theta-109\right)+2^{60} 3 x^{8}\left(2608\theta^4+4960\theta^3+8764\theta^2+4440\theta+423\right)+2^{68} 5 x^{9}\left(1216\theta^4+2592\theta^3+4596\theta^2+3456\theta+999\right)+2^{76} 5 x^{10}\left(736\theta^4+2048\theta^3+3128\theta^2+2536\theta+867\right)+2^{84} 5^{2} x^{11}\left(64\theta^4+256\theta^3+412\theta^2+312\theta+93\right)+2^{92} 5^{2} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -144, 13584, -80128, -173794032, ... --> OEIS Normalized instanton numbers (n0=1): 224, -22712, 4999008, -855952448, 199163179936, ... ; Common denominator:...
\((256z+1)^2(65536z^2+256z+1)^2(83886080z^3+768z+1)^2\)
| \(-\frac{ 1}{ 256}\) | \(-\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 3}I\) | \(-\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 3}I\) | ≈\(-0.00114\) | \(0\) | ≈\(0.00057-0.003183I\) | ≈\(0.00057+0.003183I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(3\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(4\) | \(0\) | \(4\) | \(4\) | \(\frac{ 3}{ 2}\) |
2
New Number: 12.4 | AESZ: | Superseeker: 4 -228/5 | Hash: c24070a1d4a449404cd7b46398fa6d6e
Degree: 12
\(5^{2} \theta^4-2^{2} 5^{2} x\left(16\theta^4+32\theta^3+31\theta^2+15\theta+3\right)+2^{4} 5 x^{2}\left(736\theta^4+2368\theta^3+3848\theta^2+2960\theta+915\right)-2^{10} 5 x^{3}\left(304\theta^4+1176\theta^3+2337\theta^2+2313\theta+891\right)+2^{12} 3 x^{4}\left(2608\theta^4+10688\theta^3+21652\theta^2+23580\theta+9945\right)-2^{16} 3 x^{5}\left(2784\theta^4+11616\theta^3+21812\theta^2+22396\theta+9191\right)+2^{21} 3 x^{6}\left(1232\theta^4+5232\theta^3+9332\theta^2+7968\theta+2649\right)-2^{25} 3^{2} x^{7}\left(304\theta^4+1312\theta^3+2472\theta^2+1992\theta+559\right)+2^{30} 3 x^{8}\left(280\theta^4+1216\theta^3+2491\theta^2+2337\theta+827\right)-2^{32} x^{9}\left(1664\theta^4+7200\theta^3+13692\theta^2+11988\theta+3951\right)+2^{38} x^{10}\left(164\theta^4+832\theta^3+1751\theta^2+1731\theta+663\right)-2^{40} x^{11}\left(160\theta^4+928\theta^3+2072\theta^2+2072\theta+777\right)+2^{44} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 108, 688, 3564, ... --> OEIS Normalized instanton numbers (n0=1): 4, -29/5, -228/5, 3724/5, -31856/5, ... ; Common denominator:...
\((16z-1)^2(256z^2-16z+1)^2(4096z^3-768z^2-5)^2\)
| ≈\(-0.013312-0.074322I\) | ≈\(-0.013312+0.074322I\) | \(0\) | \(\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 3}I\) | \(\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 3}I\) | \(\frac{ 1}{ 16}\) | ≈\(0.214124\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(3\) | \(3\) | \(0\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(4\) | \(4\) | \(0\) | \(1\) | \(1\) | \(1\) | \(4\) | \(\frac{ 3}{ 2}\) |
3
New Number: 12.12 | AESZ: | Superseeker: 48 3184 | Hash: 2b1c995b5f2826ce90fc016ad86fd66f
Degree: 12
\(\theta^4-2^{4} x\left(27\theta^4+42\theta^3+37\theta^2+16\theta+3\right)+2^{9} x^{2}\left(139\theta^4+430\theta^3+579\theta^2+376\theta+103\right)-2^{14} x^{3}\left(369\theta^4+1638\theta^3+2992\theta^2+2481\theta+819\right)+2^{19} x^{4}\left(667\theta^4+2870\theta^3+6158\theta^2+6571\theta+2559\right)-2^{24} x^{5}\left(1263\theta^4+3066\theta^3+2692\theta^2+4295\theta+2110\right)+2^{29} 3 x^{6}\left(787\theta^4+1842\theta^3-1598\theta^2-3339\theta-1652\right)-2^{34} x^{7}\left(3087\theta^4+9750\theta^3+2942\theta^2-13117\theta-9816\right)+2^{39} x^{8}\left(3227\theta^4+6254\theta^3+14286\theta^2+4793\theta-1948\right)-2^{44} x^{9}\left(3906\theta^4+1440\theta^3+5279\theta^2+7593\theta+3747\right)+2^{49} x^{10}\left(3896\theta^4+6208\theta^3+3391\theta^2+725\theta+525\right)-2^{54} 5 x^{11}\left(408\theta^4+1536\theta^3+2230\theta^2+1460\theta+361\right)+2^{59} 5^{2} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 48, 2704, 179968, 14147856, ... --> OEIS Normalized instanton numbers (n0=1): 48, 46, 3184, 409910, -3351792, ... ; Common denominator:...
\((16z-1)(32z-1)(4096z^2-192z+1)(64z-1)^2(163840z^3+1024z^2+32z-1)^2\)
| ≈\(-0.009802-0.019I\) | ≈\(-0.009802+0.019I\) | \(0\) | \(\frac{ 3}{ 128}-\frac{ 1}{ 128}\sqrt{ 5}\) | ≈\(0.013353\) | \(\frac{ 1}{ 64}\) | \(\frac{ 1}{ 32}\) | \(\frac{ 3}{ 128}+\frac{ 1}{ 128}\sqrt{ 5}\) | \(\frac{ 1}{ 16}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(3\) | \(3\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(4\) | \(4\) | \(0\) | \(2\) | \(4\) | \(1\) | \(2\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
4
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:...
\((64z-1)(32z-1)(256z^2-48z+1)(16z-1)^2(32768z^3-1024z^2-32z-5)^2\)
| ≈\(-0.020941-0.040594I\) | ≈\(-0.020941+0.040594I\) | \(0\) | \(\frac{ 1}{ 64}\) | \(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 32}\) | \(\frac{ 1}{ 16}\) | ≈\(0.073133\) | \(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(3\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(4\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(1\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
5
New Number: 12.16 | AESZ: | Superseeker: 288 -8252768 | Hash: e5412f8624ff9afc10459abda2d297d0
Degree: 12
\(\theta^4-2^{4} x\left(160\theta^4+224\theta^3+200\theta^2+88\theta+17\right)+2^{12} x^{2}\left(992\theta^4+1184\theta^3+1664\theta^2+1368\theta+399\right)-2^{22} x^{3}\left(1172\theta^4+1104\theta^3+542\theta^2+912\theta+331\right)+2^{28} x^{4}\left(16624\theta^4+15104\theta^3+5408\theta^2-752\theta-1829\right)-2^{37} x^{5}\left(23072\theta^4+16784\theta^3+23748\theta^2+1100\theta-4281\right)+2^{47} x^{6}\left(12696\theta^4+8556\theta^3+18218\theta^2+6591\theta+144\right)-2^{52} x^{7}\left(167440\theta^4+175808\theta^3+289048\theta^2+160176\theta+37033\right)+2^{61} x^{8}\left(96496\theta^4+172672\theta^3+241896\theta^2+158752\theta+44823\right)-2^{70} x^{9}\left(36784\theta^4+100224\theta^3+148008\theta^2+108576\theta+32891\right)+2^{79} x^{10}\left(8720\theta^4+32704\theta^3+54968\theta^2+44784\theta+14529\right)-2^{91} x^{11}\left(144\theta^4+696\theta^3+1352\theta^2+1222\theta+427\right)+2^{99} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 272, 85264, 30040320, 11678489872, ... --> OEIS Normalized instanton numbers (n0=1): 288, 59200, -8252768, -1223488576, 585571467872, ... ; Common denominator:...
\((512z-1)(65536z^2-768z+1)(134217728z^3-655360z^2+256z-1)^2(256z-1)^3\)
| \(0\) | ≈\(3.7e-05-0.001244I\) | ≈\(3.7e-05+0.001244I\) | \(\frac{ 3}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\) | \(\frac{ 1}{ 512}\) | \(\frac{ 1}{ 256}\) | ≈\(0.004808\) | \(\frac{ 3}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(3\) | \(3\) | \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(4\) | \(4\) | \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
6
New Number: 12.17 | AESZ: | Superseeker: 4 52 | Hash: e65be092d4832d3740d2a3078755f447
Degree: 12
\(\theta^4+2^{2} x\left(24\theta^4+6\theta^3+11\theta^2+8\theta+2\right)+2^{4} x^{2}\left(209\theta^4+2\theta^3+23\theta^2-10\right)+2^{7} x^{3}\left(223\theta^4-1218\theta^3-2225\theta^2-2088\theta-776\right)-2^{10} x^{4}\left(1409\theta^4+9634\theta^3+19337\theta^2+18420\theta+6872\right)-2^{13} x^{5}\left(6527\theta^4+35858\theta^3+78357\theta^2+78428\theta+30414\right)-2^{17} x^{6}\left(6276\theta^4+37704\theta^3+91143\theta^2+97914\theta+40036\right)-2^{21} x^{7}\left(2923\theta^4+22130\theta^3+61939\theta^2+73401\theta+32138\right)-2^{24} x^{8}\left(602\theta^4+10928\theta^3+42765\theta^2+60182\theta+29287\right)+2^{26} x^{9}\left(2352\theta^4+7392\theta^3-7024\theta^2-31968\theta-21891\right)+2^{29} x^{10}\left(1584\theta^4+11904\theta^3+24696\theta^2+19776\theta+4915\right)-2^{35} x^{11}\left(16\theta^4-176\theta^3-784\theta^2-1036\theta-449\right)-2^{39} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -8, 112, -1152, 19216, ... --> OEIS Normalized instanton numbers (n0=1): 4, 7/2, 52, 500, 2796, ... ; Common denominator:...
\(-(8z+1)(256z^2+16z-1)(1024z^3-160z^2-28z-1)^2(16z+1)^3\)
| \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(-\frac{ 1}{ 16}\) | ≈\(-0.057187-0.018391I\) | ≈\(-0.057187+0.018391I\) | \(0\) | \(-\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | ≈\(0.270624\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(0\) | \(1\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(4\) | \(0\) | \(2\) | \(4\) | \(\frac{ 3}{ 2}\) |
7
New Number: 12.2 | AESZ: | Superseeker: 64 39744 | Hash: b92032007ecbbf3af5801c4b1e4cf97a
Degree: 12
\(\theta^4+2^{5} x\theta(4\theta^3-10\theta^2-6\theta-1)-2^{8} x^{2}\left(92\theta^4+248\theta^3+200\theta^2+228\theta+89\right)-2^{14} x^{3}\left(84\theta^4+336\theta^3+664\theta^2+132\theta-51\right)+2^{18} x^{4}\left(944\theta^4+1312\theta^3+8928\theta^2+7384\theta+2567\right)-2^{26} x^{5}\left(176\theta^4-1456\theta^3-3477\theta^2-3814\theta-1741\right)-2^{32} x^{6}\left(216\theta^4+1200\theta^3+576\theta^2+1314\theta+697\right)+2^{38} x^{7}\left(456\theta^4+624\theta^3-3085\theta^2-5590\theta-3089\right)-2^{43} x^{8}\left(176\theta^4-3616\theta^3-2404\theta^2-288\theta+1027\right)-2^{50} x^{9}\left(208\theta^4+1824\theta^3+2581\theta^2+1434\theta+73\right)+2^{57} x^{10}\left(122\theta^4-44\theta^3-718\theta^2-1005\theta-410\right)-2^{62} 5 x^{11}\left(4\theta^4-32\theta^3-145\theta^2-190\theta-82\right)-2^{66} 5^{2} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 1424, 13312, 4213008, ... --> OEIS Normalized instanton numbers (n0=1): 64, -692, 39744, -2001358, 95440576, ... ; Common denominator:...
\(-(-1+64z+4096z^2)(64z-1)^2(64z+1)^2(655360z^3-4096z^2+96z+1)^2\)
| \(-\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 5}\) | \(-\frac{ 1}{ 64}\) | ≈\(-0.006598\) | \(0\) | ≈\(0.006424-0.013784I\) | ≈\(0.006424+0.013784I\) | \(-\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 5}\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(3\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(1\) | \(4\) | \(0\) | \(4\) | \(4\) | \(2\) | \(1\) | \(\frac{ 3}{ 2}\) |
8
New Number: 12.3 | AESZ: | Superseeker: -12/5 444/5 | Hash: 45726409a4c817f929c9e6e49b33a941
Degree: 12
\(5^{2} \theta^4+2^{2} 5 x\left(4\theta^4+56\theta^3+53\theta^2+25\theta+5\right)-2^{4} x^{2}\left(976\theta^4+6208\theta^3+9016\theta^2+6360\theta+1985\right)+2^{8} x^{3}\left(832\theta^4-2304\theta^3-11276\theta^2-12780\theta-5495\right)+2^{13} x^{4}\left(176\theta^4+4672\theta^3+16244\theta^2+19860\theta+9145\right)-2^{16} x^{5}\left(1824\theta^4+8448\theta^3+1052\theta^2-6884\theta-5771\right)+2^{21} x^{6}\left(432\theta^4+192\theta^3-3816\theta^2-9540\theta-5869\right)+2^{24} x^{7}\left(704\theta^4+10048\theta^3+21804\theta^2+22348\theta+7847\right)-2^{29} x^{8}\left(472\theta^4+2176\theta^3+7884\theta^2+11644\theta+5965\right)+2^{32} x^{9}\left(336\theta^4+672\theta^3+1144\theta^2+2904\theta+2145\right)+2^{36} x^{10}\left(368\theta^4+1216\theta^3+1304\theta^2-240\theta-697\right)-2^{44} x^{11}(2\theta+3)(4\theta^3+28\theta^2+51\theta+28)-2^{46} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -4, 108, -912, 21484, ... --> OEIS Normalized instanton numbers (n0=1): -12/5, 103/5, 444/5, 1148/5, -6704, ... ; Common denominator:...
\(-(-1-16z+256z^2)(16z+1)^2(16z-1)^2(8192z^3+768z^2-32z+5)^2\)
| ≈\(-0.148005\) | \(-\frac{ 1}{ 16}\) | \(\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(0\) | ≈\(0.027128-0.058206I\) | ≈\(0.027128+0.058206I\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(3\) | \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(4\) | \(1\) | \(2\) | \(0\) | \(4\) | \(4\) | \(1\) | \(2\) | \(\frac{ 3}{ 2}\) |
9
New Number: 13.4 | AESZ: | Superseeker: 128 341632 | Hash: e2189010cb583bd9f4eab25b75b409cf
Degree: 13
\(\theta^4-2^{5} x\left(4\theta^4+34\theta^3+28\theta^2+11\theta+2\right)-2^{8} x^{2}\left(380\theta^4-872\theta^3-2096\theta^2-1252\theta-351\right)+2^{14} x^{3}\left(1572\theta^4+2760\theta^3-6140\theta^2-4788\theta-1727\right)+2^{18} x^{4}\left(112\theta^4-71968\theta^3+30800\theta^2+34304\theta+16775\right)-2^{25} x^{5}\left(25792\theta^4-66000\theta^3+21380\theta^2+29896\theta+17669\right)+2^{30} x^{6}\left(147184\theta^4-74240\theta^3+128248\theta^2+131808\theta+68259\right)-2^{36} x^{7}\left(204848\theta^4+52096\theta^3+180984\theta^2+135280\theta+61687\right)+2^{42} x^{8}\left(149520\theta^4+15104\theta^3-78056\theta^2-161888\theta-66647\right)-2^{49} x^{9}\left(15408\theta^4-100672\theta^3-280440\theta^2-315312\theta-124965\right)-2^{56} x^{10}\left(10256\theta^4+80960\theta^3+191000\theta^2+198384\theta+76409\right)+2^{63} x^{11}\left(4880\theta^4+28864\theta^3+65080\theta^2+65776\theta+24913\right)-2^{73} x^{12}\left(112\theta^4+648\theta^3+1448\theta^2+1450\theta+545\right)+2^{79} x^{13}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 64, 4496, 339968, 27330832, ... --> OEIS Normalized instanton numbers (n0=1): 128, -4796, 341632, -31623118, 3395329408, ... ; Common denominator:...
\((128z-1)(4096z^2+64z-1)(1048576z^3-28672z^2+160z+1)^2(64z-1)^4\)
| \(-\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 5}\) | ≈\(-0.003609\) | \(0\) | \(\frac{ 1}{ 128}\) | \(-\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 5}\) | ≈\(0.015476-0.004977I\) | ≈\(0.015476+0.004977I\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(4\) | \(0\) | \(\frac{ 3}{ 2}\) |
10
New Number: 6.36 | AESZ: | Superseeker: 10/7 508/7 | Hash: b890cacbc73012eb6554263c3ea04707
Degree: 6
\(7^{2} \theta^4-2 7 x\left(60\theta^4+24\theta^3-9\theta^2-21\theta-7\right)-2^{2} x^{2}\left(6492\theta^4+30192\theta^3+46665\theta^2+30786\theta+7777\right)+2^{4} x^{3}\left(3632\theta^4-27552\theta^3-133920\theta^2-173880\theta-76083\right)+2^{9} x^{4}\left(1776\theta^4+10272\theta^3+15264\theta^2+7608\theta+121\right)-2^{14} x^{5}\left(48\theta^4-480\theta^3-2016\theta^2-2568\theta-1091\right)-2^{19} x^{6}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -2, 38, 204, 7462, ... --> OEIS Normalized instanton numbers (n0=1): 10/7, 100/7, 508/7, 808, 59910/7, ... ; Common denominator:...
\(-(16z+1)(32z-1)(4z+1)^2(32z-7)^2\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 16}\) | \(0\) | \(\frac{ 1}{ 32}\) | \(\frac{ 7}{ 32}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(-\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(\frac{ 3}{ 2}\) | \(2\) | \(0\) | \(2\) | \(4\) | \(\frac{ 3}{ 2}\) |
11
New Number: 6.37 | AESZ: | Superseeker: 80 249872 | Hash: 0c2998041752cbd976fcc2e18f2072ad
Degree: 6
\(\theta^4-2^{4} x\left(6\theta^4+96\theta^3+99\theta^2+51\theta+11\right)-2^{9} x^{2}\left(222\theta^4+48\theta^3-873\theta^2-897\theta-328\right)+2^{14} x^{3}\left(454\theta^4+6168\theta^3+4887\theta^2+891\theta-651\right)+2^{19} x^{4}\left(6492\theta^4+8760\theta^3-1557\theta^2-6945\theta-2438\right)-2^{28} 7 x^{5}\left(60\theta^4+336\theta^3+693\theta^2+642\theta+227\right)-2^{33} 7^{2} x^{6}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 176, 35792, 7805184, 1768710928, ... --> OEIS Normalized instanton numbers (n0=1): 80, -4222, 249872, -22251117, 2195810928, ... ; Common denominator:...
\(-(32z+1)(64z-1)(224z+1)^2(256z-1)^2\)
| \(-\frac{ 1}{ 32}\) | \(-\frac{ 1}{ 224}\) | \(0\) | \(\frac{ 1}{ 256}\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(4\) | \(0\) | \(\frac{ 3}{ 2}\) | \(2\) | \(\frac{ 3}{ 2}\) |