### Summary

You searched for: superseeker=-12/11,357/11

Your search produced exactly one match

1

New Number: 8.37 |  AESZ: 345  |  Superseeker: -12/11 357/11  |  Hash: 60f282ab4e1936cd96eb5ba12983db2d

Degree: 8

$11^{2} \theta^4+3 11 x\left(113\theta^4+184\theta^3+158\theta^2+66\theta+11\right)+2 x^{2}\left(28397\theta^4+95138\theta^3+128420\theta^2+77715\theta+17622\right)-3 x^{3}\left(3165\theta^4+180822\theta^3+560611\theta^2+539022\theta+167508\right)-3 x^{4}\left(233330\theta^4+1052614\theta^3+1424797\theta^2+774518\theta+145896\right)-3^{2} x^{5}\left(12866\theta^4-98902\theta^3-52127\theta^2+102028\theta+63723\right)+3^{2} x^{6}\left(183763\theta^4+473778\theta^3+427847\theta^2+147060\theta+11268\right)-2^{3} 3^{3} x^{7}\left(5006\theta^4+13414\theta^3+14935\theta^2+8228\theta+1869\right)+2^{6} 3^{7} x^{8}\left((\theta+1)^4\right)$

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Coefficients of the holomorphic solution: 1, -3, 9, 141, -3879, ...
--> OEIS
Normalized instanton numbers (n0=1): -12/11, -28/11, 357/11, -1172/11, -5250/11, ... ; Common denominator:...

#### Discriminant

$(3z-1)(81z^3-457z^2-30z-1)(-11-21z+24z^2)^2$

#### Local exponents

$\frac{ 7}{ 16}-\frac{ 1}{ 48}\sqrt{ 1497}$ ≈$-0.032637-0.033136I$ ≈$-0.032637+0.033136I$$0$$\frac{ 1}{ 3}$$\frac{ 7}{ 16}+\frac{ 1}{ 48}\sqrt{ 1497}$ ≈$5.707249$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$1$$0$$1$$1$$1$$1$
$3$$1$$1$$0$$1$$3$$1$$1$
$4$$2$$2$$0$$2$$4$$2$$1$

#### Note:

This operator has a second MUM point at infinity corresponding to operator 8.38.