### Summary

You searched for: superseeker=11/13,385/39

Your search produced exactly one match

1

New Number: 8.35 |  AESZ: 326  |  Superseeker: 11/13 385/39  |  Hash: 946b91838924db64fe0ebdf0d473e621

Degree: 8

$13^{2} \theta^4-13 x\theta(56\theta^3+178\theta^2+115\theta+26)-x^{2}\left(28466\theta^4+109442\theta^3+165603\theta^2+117338\theta+32448\right)-x^{3}\left(233114\theta^4+1257906\theta^3+2622815\theta^2+2467842\theta+872352\right)-x^{4}\left(989585\theta^4+6852298\theta^3+17737939\theta^2+19969754\theta+8108448\right)-x^{5}(\theta+1)(2458967\theta^3+18007287\theta^2+44047582\theta+35386584)-3^{2} x^{6}(\theta+1)(\theta+2)(393163\theta^2+2539029\theta+4164444)-3^{3} 11 x^{7}(\theta+3)(\theta+2)(\theta+1)(8683\theta+34604)-3^{3} 11^{2} 13 17 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)$

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Coefficients of the holomorphic solution: 1, 0, 12, 96, 1116, ...
--> OEIS
Normalized instanton numbers (n0=1): 11/13, 30/13, 385/39, 672/13, 4437/13, ... ; Common denominator:...

#### Discriminant

$-(3z+1)(13z^2+5z+1)(153z^3+75z^2+14z-1)(13+11z)^2$

#### Local exponents

$-\frac{ 13}{ 11}$$-\frac{ 1}{ 3}$ ≈$-0.272124-0.216493I$ ≈$-0.272124+0.216493I$$-\frac{ 5}{ 26}-\frac{ 3}{ 26}\sqrt{ 3}I$$-\frac{ 5}{ 26}+\frac{ 3}{ 26}\sqrt{ 3}I$$0$ ≈$0.054052$$\infty$
$0$$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$1$$1$$1$$1$$0$$1$$2$
$3$$1$$1$$1$$1$$1$$0$$1$$3$
$4$$2$$2$$2$$2$$2$$0$$2$$4$

#### Note:

This opeerator is reducible to 6.25