### Summary

You searched for: sol=52

1

New Number: 10.6 |  AESZ:  |  Superseeker: 8 2200/9  |  Hash: b5aa0abf76ddfbd280ec220a43822aa4

Degree: 10

$\theta^4+2^{2} x\left(21\theta^4-6\theta^3+3\theta+1\right)+2^{4} x^{2}\left(126\theta^4-96\theta^3-16\theta^2-56\theta-33\right)+2^{6} x^{3}\left(84\theta^4-336\theta^3-226\theta^2-366\theta-163\right)+2^{11} 3 x^{4}\left(39\theta^4+500\theta^3+1230\theta^2+1160\theta+407\right)+2^{12} x^{5}\left(7029\theta^4+50118\theta^3+125086\theta^2+129149\theta+48902\right)+2^{14} x^{6}\left(38550\theta^4+294456\theta^3+806428\theta^2+911232\theta+368273\right)+2^{16} x^{7}\left(77544\theta^4+708720\theta^3+2233434\theta^2+2804346\theta+1214177\right)+2^{20} x^{8}\left(9171\theta^4+117228\theta^3+467444\theta^2+684316\theta+324572\right)-2^{23} x^{9}(2\theta+3)(2114\theta^3+16713\theta^2+37111\theta+22497)+2^{26} 3 5^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -4, 52, -688, 2500, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, -75/2, 2200/9, -8117/2, 47936, ... ; Common denominator:...

#### Discriminant

$(12z+1)(6400z^3+192z^2-24z+1)(16z+1)^2(32z^2-32z-1)^2$

#### Local exponents

≈$-0.090507$$-\frac{ 1}{ 12}$$-\frac{ 1}{ 16}$$\frac{ 1}{ 2}-\frac{ 3}{ 8}\sqrt{ 2}$$0$ ≈$0.030254-0.02848I$ ≈$0.030254+0.02848I$$\frac{ 1}{ 2}+\frac{ 3}{ 8}\sqrt{ 2}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$\frac{ 1}{ 2}$$1$$0$$1$$1$$1$$\frac{ 3}{ 2}$
$1$$1$$\frac{ 1}{ 2}$$3$$0$$1$$1$$3$$\frac{ 5}{ 2}$
$2$$2$$1$$4$$0$$2$$2$$4$$3$

#### Note:

This is operator "10.6" from ...

2

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 ...