1
New Number: 12.14 | AESZ: | Superseeker: 7/2 237/2 | Hash: 614b95fc4275078df0800c7546870e7f
Degree: 12
\(2^{2} \theta^4+2 x\left(74\theta^4+22\theta^3+77\theta^2+66\theta+18\right)+3^{2} x^{2}\left(97\theta^4+1206\theta^3+2235\theta^2+1750\theta+642\right)+3^{4} x^{3}\left(126\theta^4+3910\theta^3+7341\theta^2+8588\theta+3750\right)+3^{6} x^{4}\left(832\theta^4+6078\theta^3+26372\theta^2+37719\theta+21825\right)+3^{8} x^{5}\left(442\theta^4+12544\theta^3+62654\theta^2+116087\theta+78828\right)-3^{10} x^{6}\left(1032\theta^4-5126\theta^3-73629\theta^2-192529\theta-165306\right)-2 3^{12} x^{7}\left(1432\theta^4+11737\theta^3+11907\theta^2-41634\theta-71496\right)-3^{14} x^{8}\left(1871\theta^4+35422\theta^3+145979\theta^2+220752\theta+99504\right)+2 3^{17} x^{9}\left(151\theta^4-2094\theta^3-20341\theta^2-54972\theta-48672\right)+2^{3} 3^{19} x^{10}(\theta+3)(86\theta^3+414\theta^2+181\theta-936)+2^{3} 3^{22} x^{11}(\theta+4)(\theta+3)(21\theta^2+137\theta+224)+2^{4} 3^{24} x^{12}(\theta+3)(\theta+5)(\theta+4)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -9, -18, 747, -5751, ... --> OEIS Normalized instanton numbers (n0=1): 7/2, -193/8, 237/2, -6119/4, 16307, ... ; Common denominator:...
\((9z+1)(z+1)(324z^2-18z+1)(81z^2+9z+1)^2(486z^2-27z-2)^2\)
| \(0\) | \(\infty\) | \(\frac{ 1}{ 36}-\frac{ 1}{ 108}\sqrt{ 57}\) | \(\frac{ 1}{ 36}+\frac{ 1}{ 36}\sqrt{ 3}I\) | \(\frac{ 1}{ 36}-\frac{ 1}{ 36}\sqrt{ 3}I\) | \(-\frac{ 1}{ 18}+\frac{ 1}{ 18}\sqrt{ 3}I\) | \(\frac{ 1}{ 36}+\frac{ 1}{ 108}\sqrt{ 57}\) | \(-\frac{ 1}{ 9}\) | \(-1\) | \(-\frac{ 1}{ 18}-\frac{ 1}{ 18}\sqrt{ 3}I\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(3\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(4\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(0\) |
| \(0\) | \(4\) | \(3\) | \(1\) | \(1\) | \(-1\) | \(3\) | \(1\) | \(1\) | \(-1\) |
| \(0\) | \(5\) | \(4\) | \(2\) | \(2\) | \(1\) | \(4\) | \(2\) | \(2\) | \(1\) |
2
New Number: 13.2 | AESZ: | Superseeker: 288 -8252768 | Hash: ad47c122958add1c452a9858793ef177
Degree: 13
\(\theta^4-2^{4} x\left(192\theta^4+352\theta^3+392\theta^2+216\theta+49\right)+2^{12} x^{2}\left(1312\theta^4+2912\theta^3+5328\theta^2+4968\theta+1777\right)-2^{21} x^{3}\left(3336\theta^4+7360\theta^3+12252\theta^2+14040\theta+6269\right)+2^{28} x^{4}\left(26000\theta^4+61440\theta^3+92496\theta^2+79216\theta+30659\right)-2^{38} x^{5}\left(19848\theta^4+49192\theta^3+87106\theta^2+61486\theta+15137\right)+2^{46} x^{6}\left(48464\theta^4+126184\theta^3+248968\theta^2+204418\theta+60711\right)-2^{52} x^{7}\left(370576\theta^4+1125248\theta^3+2210040\theta^2+2071840\theta+776313\right)+2^{64} x^{8}\left(32992\theta^4+127280\theta^3+257876\theta^2+261776\theta+109291\right)-2^{71} x^{9}\left(66640\theta^4+329440\theta^3+743448\theta^2+827560\theta+373765\right)+2^{81} x^{10}\left(11376\theta^4+70016\theta^3+181088\theta^2+224296\theta+110253\right)-2^{88} x^{11}\left(9872\theta^4+73152\theta^3+216216\theta^2+297488\theta+159121\right)+2^{99} x^{12}\left(304\theta^4+2640\theta^3+8824\theta^2+13396\theta+7763\right)-2^{108} x^{13}\left((2\theta+5)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 784, 486672, 279216384, 154637278480, ... --> OEIS Normalized instanton numbers (n0=1): 288, 59200, -8252768, -1223488576, 585571467872, ... ; Common denominator:...
\(-(1-768z+65536z^2)(512z-1)^2(134217728z^3-655360z^2+256z-1)^2(256z-1)^3\)
| \(0\) | \(\frac{ 1}{ 512}\) | \(\infty\) | \(\frac{ 1}{ 256}\) | ≈\(3.7e-05+0.001244I\) | \(\frac{ 3}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\) | \(\frac{ 3}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\) | ≈\(3.7e-05-0.001244I\) | ≈\(0.004808\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(\frac{ 5}{ 2}\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(0\) | \(\frac{ 5}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(-1\) | \(\frac{ 5}{ 2}\) | \(0\) | \(3\) | \(1\) | \(1\) | \(3\) | \(3\) |
| \(0\) | \(1\) | \(\frac{ 5}{ 2}\) | \(0\) | \(4\) | \(2\) | \(2\) | \(4\) | \(4\) |
3
New Number: 13.3 | AESZ: | Superseeker: 4 52 | Hash: 9127ce057848ca38f220a7bb67e245a2
Degree: 13
\(\theta^4-2^{2} x\left(38\theta^4+50\theta^3+53\theta^2+28\theta+6\right)+2^{4} x^{2}\left(617\theta^4+1598\theta^3+2361\theta^2+1812\theta+586\right)-2^{8} x^{3}\left(1422\theta^4+5468\theta^3+10321\theta^2+9918\theta+3961\right)+2^{11} x^{4}\left(4165\theta^4+21060\theta^3+48228\theta^2+54855\theta+25440\right)-2^{14} x^{5}\left(8248\theta^4+50660\theta^3+135119\theta^2+175776\theta+91644\right)+2^{16} x^{6}\left(23161\theta^4+161282\theta^3+479205\theta^2+690060\theta+393943\right)-2^{20} x^{7}\left(12116\theta^4+89614\theta^3+279997\theta^2+425868\theta+256804\right)+2^{23} x^{8}\left(9924\theta^4+74644\theta^3+231233\theta^2+346097\theta+206261\right)-2^{27} x^{9}\left(3250\theta^4+24820\theta^3+75837\theta^2+107033\theta+58293\right)+2^{28} x^{10}\left(6672\theta^4+52000\theta^3+164304\theta^2+235440\theta+126113\right)-2^{32} x^{11}\left(1312\theta^4+10208\theta^3+32688\theta^2+49072\theta+28407\right)+2^{36} x^{12}\left(192\theta^4+1568\theta^3+4952\theta^2+7144\theta+3959\right)-2^{40} x^{13}\left((2\theta+5)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 24, 464, 8832, 178960, ... --> OEIS Normalized instanton numbers (n0=1): 4, 7/2, 52, 500, 2796, ... ; Common denominator:...
\(-(1-48z+256z^2)(8z-1)^2(512z^3-32z^2+20z-1)^2(16z-1)^3\)
| \(0\) | ≈\(0.005863+0.196043I\) | \(\infty\) | ≈\(0.005863-0.196043I\) | ≈\(0.050774\) | \(\frac{ 1}{ 8}\) | \(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(\frac{ 5}{ 2}\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(1\) | \(\frac{ 5}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(0\) | \(1\) |
| \(0\) | \(3\) | \(\frac{ 5}{ 2}\) | \(3\) | \(3\) | \(-1\) | \(1\) | \(0\) | \(1\) |
| \(0\) | \(4\) | \(\frac{ 5}{ 2}\) | \(4\) | \(4\) | \(1\) | \(2\) | \(0\) | \(2\) |
4
New Number: 14.1 | AESZ: | Superseeker: 0 0 | Hash: a8cf56492aecc07971e82c9104785180
Degree: 14
\(\theta^4-x\left(13\theta^4+14\theta^3+16\theta^2+9\theta+2\right)+x^{2}\left(33\theta^4-88\theta^3-265\theta^2-324\theta-148\right)+x^{3}\left(217\theta^4+2362\theta^3+6403\theta^2+8178\theta+4160\right)-2 x^{4}\left(677\theta^4+4134\theta^3+8089\theta^2+6210\theta+360\right)+2^{2} 3 x^{5}\left(151\theta^4-1266\theta^3-11610\theta^2-28955\theta-25110\right)+2^{2} x^{6}\left(1895\theta^4+37302\theta^3+176991\theta^2+355848\theta+268836\right)-2^{2} x^{7}\left(9635\theta^4+89170\theta^3+185885\theta^2-107394\theta-522464\right)+2^{3} x^{8}\left(5907\theta^4-10636\theta^3-416125\theta^2-1666326\theta-2051920\right)+2^{5} x^{9}\left(2947\theta^4+80284\theta^3+519934\theta^2+1328475\theta+1205150\right)-2^{6} x^{10}\left(6122\theta^4+84852\theta^3+397555\theta^2+722745\theta+356430\right)+2^{6} 3 x^{11}\left(2259\theta^4+13398\theta^3-46549\theta^2-456244\theta-796656\right)+2^{7} 3^{2} x^{12}(\theta+4)(371\theta^3+8580\theta^2+53325\theta+101564)-2^{10} 3^{3} x^{13}(\theta+4)(\theta+5)(51\theta^2+519\theta+1330)+2^{11} 3^{4} 5 x^{14}(\theta+4)(\theta+5)^2(\theta+6)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 2, 16, 48, 264, ... --> OEIS Normalized instanton numbers (n0=1): 0, 1/4, 0, -1/2, 0, ... ; Common denominator:...
\((z-1)(6z-1)(4z-1)(3z+1)(4z+1)(5z-1)(2z+1)^2(2z-1)^2(6z^2-2z+1)^2\)
| \(0\) | \(\frac{ 1}{ 6}\) | \(\frac{ 1}{ 5}\) | \(\frac{ 1}{ 4}\) | \(\infty\) | \(\frac{ 1}{ 2}\) | \(1\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 1}{ 6}-\frac{ 1}{ 6}\sqrt{ 5}I\) | \(-\frac{ 1}{ 3}\) | \(\frac{ 1}{ 6}+\frac{ 1}{ 6}\sqrt{ 5}I\) | \(-\frac{ 1}{ 4}\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(4\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(5\) | \(0\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(5\) | \(-1\) | \(1\) | \(-1\) | \(3\) | \(1\) | \(3\) | \(1\) |
| \(0\) | \(2\) | \(2\) | \(2\) | \(6\) | \(1\) | \(2\) | \(1\) | \(4\) | \(2\) | \(4\) | \(2\) |
5
New Number: 15.1 | AESZ: | Superseeker: 7/2 237/2 | Hash: df146e1b37d7a257f905c6707b923620
Degree: 15
\(2^{2} 5^{30} \theta^4-2 5^{28} x\left(3640\theta^4+11006\theta^3+13879\theta^2+8376\theta+1980\right)+3^{2} 5^{26} x^{2}\left(538345\theta^4+4434106\theta^3+9865547\theta^2+10318472\theta+4308060\right)-3^{4} 5^{24} x^{3}\left(6742465\theta^4+323187588\theta^3+1293374270\theta^2+2006832192\theta+1174440960\right)-3^{7} 5^{22} x^{4}\left(526873995\theta^4-1668961078\theta^3-24223747379\theta^2-58879161136\theta-47787749580\right)+3^{8} 5^{20} x^{5}\left(112183726219\theta^4+702881575498\theta^3-655695079267\theta^2-6796301255992\theta-8645676874410\right)-3^{10} 5^{18} x^{6}\left(2728176480430\theta^4+50098509218682\theta^3+140700841079393\theta^2+45277394357802\theta-187513884611415\right)-3^{12} 5^{16} x^{7}\left(34762414267630\theta^4-1334642903889766\theta^3-8286651788306957\theta^2-15990739837380612\theta-8287376192342010\right)+3^{15} 5^{14} x^{8}\left(1629579653924345\theta^4+954388085050194\theta^3-55618872802839705\theta^2-207693840516161754\theta-214442659712419520\right)-3^{17} 5^{12} x^{9}\left(65369060331963795\theta^4+512595644471686042\theta^3+992825405643594911\theta^2-1201538784520100286\theta-4009291166039086080\right)+3^{20} 5^{10} x^{10}\left(534261782717034863\theta^4+6643553399420804992\theta^3+30007608488826895812\theta^2+55818610344670779952\theta+32009410686899411085\right)-3^{22} 5^{8} x^{11}\left(8440215529571954655\theta^4+138165063547130806682\theta^3+847930452008770373373\theta^2+2305208800672476166582\theta+2332526675705017692360\right)+2^{2} 3^{25} 5^{6} x^{12}(\theta+5)(6822457746356194860\theta^3+105594221828043028718\theta^2+542119266560031019991\theta+926555809752183305931)-2^{2} 3^{27} 5^{4} x^{13}(\theta+5)(\theta+6)(15337273149232082245\theta^2+289665397258229241319\theta+1092956642701689252996)-2^{5} 3^{30} 5^{2} 7 163 4447 x^{14}(\theta+5)(\theta+6)(\theta+7)(4612345059685\theta+22748051972446)+2^{12} 3^{33} 7^{2} 17 163^{2} 1213 4447^{2} x^{15}(\theta+5)(\theta+6)(\theta+7)(\theta+8)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 198/5, 119412/125, 59226669/3125, 27037427724/78125, ... --> OEIS Normalized instanton numbers (n0=1): 7/2, -193/8, 237/2, -6119/4, 16307, ... ; Common denominator:...
\((128z-25)(72z+25)(153z-25)(294759z^2-18900z+625)(378z-25)^2(39609z^2-2025z+625)^2(360207z^2-1575z-1250)^2\)
| \(0\) | \(\frac{ 25}{ 153}\) | \(\frac{ 175}{ 80046}-\frac{ 625}{ 80046}\sqrt{ 57}\) | \(\infty\) | \(\frac{ 25}{ 978}-\frac{ 625}{ 8802}\sqrt{ 3}I\) | \(\frac{ 175}{ 80046}+\frac{ 625}{ 80046}\sqrt{ 57}\) | \(\frac{ 25}{ 978}+\frac{ 625}{ 8802}\sqrt{ 3}I\) | \(\frac{ 25}{ 378}\) | \(\frac{ 25}{ 128}\) | \(-\frac{ 25}{ 72}\) | \(\frac{ 350}{ 10917}-\frac{ 625}{ 32751}\sqrt{ 3}I\) | \(\frac{ 350}{ 10917}+\frac{ 625}{ 32751}\sqrt{ 3}I\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(5\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(1\) | \(1\) | \(6\) | \(0\) | \(1\) | \(0\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(7\) | \(-1\) | \(3\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(2\) | \(4\) | \(8\) | \(1\) | \(4\) | \(1\) | \(-2\) | \(2\) | \(2\) | \(2\) | \(2\) |
6
New Number: 8.55 | AESZ: | Superseeker: 1 68/9 | Hash: 39ed8ce7572bc79a333f77c892033bcf
Degree: 8
\(\theta^4-x\left(33\theta^4+98\theta^3+105\theta^2+56\theta+12\right)+2^{3} x^{2}\left(34\theta^4+276\theta^3+609\theta^2+582\theta+216\right)+2^{4} 3 x^{3}\left(11\theta^4-170\theta^3-941\theta^2-1520\theta-846\right)-2^{7} 3^{2} x^{4}(2\theta^2+6\theta+5)(4\theta^2+12\theta-31)+2^{8} 3 x^{5}\left(11\theta^4+302\theta^3+1183\theta^2+1652\theta+726\right)+2^{11} x^{6}\left(34\theta^4+132\theta^3-39\theta^2-708\theta-747\right)-2^{12} x^{7}\left(33\theta^4+298\theta^3+1005\theta^2+1492\theta+816\right)+2^{16} x^{8}\left((\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 120, 1216, 13080, ... --> OEIS Normalized instanton numbers (n0=1): 1, -2, 68/9, -30, 150, ... ; Common denominator:...
\((z-1)(16z-1)(16z^2-16z+1)(4z-1)^2(4z+1)^2\)
| \(0\) | \(1\) | \(\frac{ 1}{ 4}\) | \(\infty\) | \(\frac{ 1}{ 2}-\frac{ 1}{ 4}\sqrt{ 3}\) | \(\frac{ 1}{ 2}+\frac{ 1}{ 4}\sqrt{ 3}\) | \(-\frac{ 1}{ 4}\) | \(\frac{ 1}{ 16}\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(3\) | \(0\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(1\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(-1\) | \(3\) | \(1\) | \(1\) | \(3\) | \(1\) |
| \(0\) | \(2\) | \(1\) | \(3\) | \(2\) | \(2\) | \(4\) | \(2\) |