Summary

You searched for: sol=464

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1

New Number: 5.9 |  AESZ: 56  |  Superseeker: -16 -3280  |  Hash: 58a7f24bf18cb98b526885069667f9f0  

Degree: 5

\(\theta^4-2^{4} x\left(22\theta^4+8\theta^3+9\theta^2+5\theta+1\right)+2^{9} x^{2}\left(94\theta^4+88\theta^3+97\theta^2+45\theta+8\right)-2^{14} x^{3}\left(194\theta^4+336\theta^3+371\theta^2+195\theta+41\right)+2^{19} 3 x^{4}\left(64\theta^4+176\theta^3+217\theta^2+129\theta+30\right)-2^{27} 3^{2} x^{5}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 16, 464, 17152, 725776, ...
--> OEIS
Normalized instanton numbers (n0=1): -16, -178, -3280, -76197, -2046896, ... ; Common denominator:...

Discriminant

\(-(-1+32z)(96z-1)^2(64z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 96}\)\(\frac{ 1}{ 64}\)\(\frac{ 1}{ 32}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)
\(0\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)
\(0\)\(4\)\(1\)\(2\)\(1\)

Note:

There is a second MUM-point hiding at infinity, corresponding to Operator...

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2

New Number: 13.3 |  AESZ:  |  Superseeker: 4 52  |  Hash: 9127ce057848ca38f220a7bb67e245a2  

Degree: 13

\(\theta^4-2^{2} x\left(38\theta^4+50\theta^3+53\theta^2+28\theta+6\right)+2^{4} x^{2}\left(617\theta^4+1598\theta^3+2361\theta^2+1812\theta+586\right)-2^{8} x^{3}\left(1422\theta^4+5468\theta^3+10321\theta^2+9918\theta+3961\right)+2^{11} x^{4}\left(4165\theta^4+21060\theta^3+48228\theta^2+54855\theta+25440\right)-2^{14} x^{5}\left(8248\theta^4+50660\theta^3+135119\theta^2+175776\theta+91644\right)+2^{16} x^{6}\left(23161\theta^4+161282\theta^3+479205\theta^2+690060\theta+393943\right)-2^{20} x^{7}\left(12116\theta^4+89614\theta^3+279997\theta^2+425868\theta+256804\right)+2^{23} x^{8}\left(9924\theta^4+74644\theta^3+231233\theta^2+346097\theta+206261\right)-2^{27} x^{9}\left(3250\theta^4+24820\theta^3+75837\theta^2+107033\theta+58293\right)+2^{28} x^{10}\left(6672\theta^4+52000\theta^3+164304\theta^2+235440\theta+126113\right)-2^{32} x^{11}\left(1312\theta^4+10208\theta^3+32688\theta^2+49072\theta+28407\right)+2^{36} x^{12}\left(192\theta^4+1568\theta^3+4952\theta^2+7144\theta+3959\right)-2^{40} x^{13}\left((2\theta+5)^4\right)\)

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Coefficients of the holomorphic solution: 1, 24, 464, 8832, 178960, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 7/2, 52, 500, 2796, ... ; Common denominator:...

Discriminant

\(-(1-48z+256z^2)(8z-1)^2(512z^3-32z^2+20z-1)^2(16z-1)^3\)

Local exponents

\(0\) ≈\(0.005863-0.196043I\) ≈\(0.005863+0.196043I\)\(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) ≈\(0.050774\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 8}\)\(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 5}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(0\)\(0\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(3\)\(3\)\(1\)\(3\)\(0\)\(-1\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(4\)\(4\)\(2\)\(4\)\(0\)\(1\)\(2\)\(\frac{ 5}{ 2}\)

Note:

This is operator "13.3" from ...

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3

New Number: 8.45 |  AESZ:  |  Superseeker: -12/5 -20  |  Hash: 52e4f6959f297529016ddef66a399c12  

Degree: 8

\(5^{2} \theta^4+2^{2} 5 x\left(19\theta^4+86\theta^3+73\theta^2+30\theta+5\right)+2^{4} x^{2}\left(709\theta^4+4252\theta^3+7339\theta^2+4830\theta+1165\right)-2^{8} x^{3}\left(420\theta^4+114\theta^3-3294\theta^2-3960\theta-1325\right)-2^{10} x^{4}\left(949\theta^4+6782\theta^3+11350\theta^2+7719\theta+1889\right)+2^{12} x^{5}\left(1315\theta^4+4282\theta^3+7199\theta^2+5744\theta+1691\right)+2^{14} x^{6}\left(613\theta^4+1560\theta^3+973\theta^2-216\theta-249\right)+2^{18} x^{7}\left(11\theta^4-2\theta^3-40\theta^2-39\theta-11\right)-2^{20} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, -4, -4, 464, -4244, ...
--> OEIS
Normalized instanton numbers (n0=1): -12/5, -83/5, -20, 3941/20, -13872/5, ... ; Common denominator:...

Discriminant

\(-(8z+1)(128z^3-624z^2-20z-1)(-5+32z+32z^2)^2\)

Local exponents

\(-\frac{ 1}{ 2}-\frac{ 1}{ 8}\sqrt{ 26}\)\(-\frac{ 1}{ 8}\) ≈\(-0.016083-0.036516I\) ≈\(-0.016083+0.036516I\)\(0\)\(-\frac{ 1}{ 2}+\frac{ 1}{ 8}\sqrt{ 26}\) ≈\(4.907166\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(1\)\(1\)\(0\)\(3\)\(1\)\(1\)
\(4\)\(2\)\(2\)\(2\)\(0\)\(4\)\(2\)\(1\)

Note:

This is operator "8.45" from ...

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4

New Number: 24.14 |  AESZ:  |  Superseeker: 16/3 -880/81  |  Hash: 13173bd8cb75baee8a898c9c6303c117  

Degree: 24

\(3^{3} \theta^4-2^{2} 3^{2} x\left(30\theta^4+68\theta^3+54\theta^2+20\theta+3\right)+2^{4} 3 x^{2}\left(129\theta^4+1036\theta^3+1445\theta^2+626\theta+57\right)+2^{6} x^{3}\left(6560\theta^4+16168\theta^3+28438\theta^2+29162\theta+11793\right)-2^{10} x^{4}\left(4293\theta^4-840\theta^3-26162\theta^2-17539\theta-3471\right)+2^{10} x^{5}\left(4576\theta^4-45960\theta^3-527326\theta^2-531090\theta-17739\right)+2^{12} x^{6}\left(253469\theta^4+268652\theta^3-420979\theta^2-1072742\theta-642319\right)-2^{14} x^{7}\left(268866\theta^4-966996\theta^3-216550\theta^2-153200\theta-178363\right)-2^{16} x^{8}\left(275621\theta^4+368724\theta^3+3817808\theta^2+1152648\theta-238416\right)+2^{19} x^{9}\left(1243022\theta^4-155108\theta^3-180362\theta^2+244748\theta+432025\right)+2^{21} x^{10}\left(71199\theta^4+1979580\theta^3+6105329\theta^2+7846418\theta+3871903\right)-2^{23} x^{11}\left(2529316\theta^4+8376456\theta^3+16354702\theta^2+16114830\theta+6536563\right)-2^{27} x^{12}\left(6408\theta^4-138306\theta^3+103491\theta^2+823698\theta+691409\right)+2^{27} x^{13}\left(2135212\theta^4+13297720\theta^3+38159702\theta^2+52119782\theta+27312351\right)-2^{29} x^{14}\left(16747\theta^4+2690700\theta^3+12019727\theta^2+19459890\theta+113394717\right)-2^{31} x^{15}\left(904020\theta^4+7252460\theta^3+24658966\theta^2+39551016\theta+23394717\right)-2^{32} x^{16}\left(80943\theta^4-2350848\theta^3-16468568\theta^2-35556904\theta-24607808\right)+2^{34} x^{17}\left(439874\theta^4+3498636\theta^3+9750362\theta^2+12302316\theta+5737785\right)+2^{36} x^{18}\left(71951\theta^4+208996\theta^3-152285\theta^2-1478458\theta-1394681\right)-2^{38} x^{19}\left(76872\theta^4+678456\theta^3+1854170\theta^2+1720414\theta+306971\right)-2^{42} x^{20}\left(2563\theta^4+5100\theta^3+1540\theta^2-9969\theta-11723\right)+2^{42} x^{21}\left(5752\theta^4+39608\theta^3+102098\theta^2+114550\theta+48355\right)+2^{44} x^{22}\left(1489\theta^4+8620\theta^3+16833\theta^2+13450\theta+3789\right)-2^{46} 5 x^{23}\left(106\theta^4+684\theta^3+1682\theta^2+1872\theta+797\right)+2^{48} 5^{2} x^{24}\left((\theta+2)^4\right)\)

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Coefficients of the holomorphic solution: 1, 4, 52, 464, 1412, ...
--> OEIS
Normalized instanton numbers (n0=1): 16/3, -133/18, -880/81, -247636/243, 44329772416/11390625, ... ; Common denominator:...

Discriminant

\(27-1080z+26194765020135424z^22-37295434414161920z^23+7036874417766400z^24+1038209024z^6-4405100544z^7-18063097856z^8+651701518336z^9+149315125248z^10-347647537840128z^16+7556977777442816z^17+6192z^2+419840z^3-4396032z^4+4685824z^5+4944435070631936z^18-21217440432128z^11-860067201024z^12+286583303438336z^13-8990977163264z^14-1941368167464960z^15-21130414462599168z^19-11272193207959552z^20+25297563531870208z^21\)

No data for singularities

Note:

This is operator "24.14" from ...

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