1
New Number: 13.13 | AESZ: | Superseeker: 32 74144 | Hash: e20067c633b6371dc19f760a1140f0e4
Degree: 13
\(\theta^4-2^{3} x\left(74\theta^4+52\theta^3+70\theta^2+44\theta+11\right)+2^{6} x^{2}\left(1948\theta^4+2320\theta^3+3750\theta^2+3244\theta+1117\right)-2^{11} x^{3}\left(5498\theta^4+9708\theta^3+17699\theta^2+12099\theta+2024\right)+2^{12} x^{4}\left(90192\theta^4+243456\theta^3+317216\theta^2-2080\theta-132883\right)+2^{16} x^{5}\left(35024\theta^4+171680\theta^3+1168736\theta^2+2029296\theta+1162051\right)-2^{20} x^{6}\left(249200\theta^4+1529280\theta^3+3887240\theta^2+5111280\theta+2830091\right)+2^{24} x^{7}\left(6224\theta^4+297952\theta^3+1078344\theta^2+1331848\theta+442349\right)+2^{29} x^{8}\left(78896\theta^4+725696\theta^3+2501496\theta^2+3908720\theta+2314163\right)+2^{34} x^{9}\left(9584\theta^4+62208\theta^3+120960\theta^2+36216\theta-71103\right)+2^{38} x^{10}\left(2864\theta^4+44992\theta^3+291624\theta^2+843472\theta+893907\right)-2^{42} x^{11}\left(8176\theta^4+131296\theta^3+780536\theta^2+2035976\theta+1968867\right)-2^{47} 3 x^{12}\left(752\theta^4+11328\theta^3+62952\theta^2+153648\theta+139383\right)-2^{52} 3^{2} x^{13}\left((2\theta+7)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 88, 6576, 475776, 37804816, ... --> OEIS Normalized instanton numbers (n0=1): 32, 1048, 74144, 7046865, 788076384, ... ; Common denominator:...
\(-(16z-1)(262144z^4-8192z^3+2304z^2-256z+1)(48z-1)^2(16z+1)^2(512z^2+128z-1)^2\)
| \(-\frac{ 1}{ 8}-\frac{ 3}{ 32}\sqrt{ 2}\) | \(-\frac{ 1}{ 16}\) | ≈\(-0.024399\) | ≈\(-0.024399\) | \(0\) | ≈\(0.004052\) | \(-\frac{ 1}{ 8}+\frac{ 3}{ 32}\sqrt{ 2}\) | \(\frac{ 1}{ 48}\) | \(\frac{ 1}{ 16}\) | ≈\(0.075996\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 7}{ 2}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(-2\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(4\) | \(1\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(3\) | \(2\) | \(2\) | \(\frac{ 7}{ 2}\) |
2
New Number: 18.1 | AESZ: | Superseeker: 32 74144 | Hash: f898da39070d0f65b96891f225273ac8
Degree: 18
\(3^{36} \theta^4-2^{4} 3^{34} x\left(333\theta^4-14\theta^3-52\theta^2-45\theta-11\right)+2^{9} 3^{32} x^{2}\left(19692\theta^4-14974\theta^3-24933\theta^2-14648\theta-2899\right)-2^{13} 3^{30} x^{3}\left(978450\theta^4-2297356\theta^3-2203108\theta^2-351038\theta+150293\right)+2^{16} 3^{28} x^{4}\left(29162034\theta^4-228074816\theta^3-41034760\theta^2+129318642\theta+56632337\right)+2^{20} 3^{26} x^{5}\left(587116062\theta^4+2884581236\theta^3-5110414872\theta^2-4354953074\theta-719634683\right)-2^{25} 3^{24} x^{6}\left(7788212430\theta^4-25994187260\theta^3-36307798646\theta^2+22596130679\theta+17870398220\right)-2^{30} 3^{22} x^{7}\left(24952379517\theta^4+215382922768\theta^3-193917927994\theta^2+68687254791\theta+118177203129\right)+2^{32} 3^{20} x^{8}\left(2465059314285\theta^4-6257533070480\theta^3-160224268608\theta^2-2321915485018\theta-2939103970827\right)+2^{36} 3^{18} x^{9}\left(19196808612383\theta^4+40471527323966\theta^3+47011511994668\theta^2+29979826610437\theta-3798547377438\right)-2^{41} 3^{16} x^{10}\left(31815915596118\theta^4-91985871789250\theta^3-243694332457379\theta^2-412337070880227\theta-225096344703166\right)-2^{47} 3^{14} x^{11}\left(152409250801971\theta^4+392522456009119\theta^3+483307141123011\theta^2-23876260594498\theta-261430636861709\right)-2^{52} 3^{12} x^{12}\left(341239631092419\theta^4+2089976311699567\theta^3+6237679550918137\theta^2+8770476560885579\theta+4635246761447824\right)+2^{56} 3^{10} x^{13}\left(529561889839080\theta^4+2701783513427734\theta^3+2623668209036513\theta^2-4470872132749815\theta-6908279580524476\right)+2^{61} 3^{8} x^{14}\left(5372561842952418\theta^4+44975097147122878\theta^3+143025130667911083\theta^2+203932774055033813\theta+109645866522838268\right)+2^{67} 3^{6} x^{15}(\theta+2)(4847763038128923\theta^3+36798926507269013\theta^2+95492964503573704\theta+84453090506711840)+2^{72} 3^{4} 5 13 x^{16}(\theta+2)(\theta+3)(58496948477298\theta^2+345543721824865\theta+525022379845215)+2^{76} 3^{2} 5^{2} 13^{2} 233 x^{17}(\theta+2)(\theta+3)(\theta+4)(2800175409\theta+9490253627)+2^{83} 5^{3} 13^{3} 233^{2} 6343 x^{18}(\theta+2)(\theta+3)(\theta+4)(\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -176/9, 18544/27, 27113216/729, 43446571280/6561, ... --> OEIS Normalized instanton numbers (n0=1): 32, 1048, 74144, 7046865, 788076384, ... ; Common denominator:...
\((128z-9)(1662779392z^4-15777792z^3+6283008z^2-1632960z+6561)(-81+10080z+59648z^2)^2(416z-9)^3(160z+9)^3(16z+9)^3\)
No data for singularities