### Summary

You searched for: inst=-80

1

New Number: 5.13 |  AESZ: 83  |  Superseeker: -80 -174096  |  Hash: 171e1251d8e4f7de878d0d07de6f58ab

Degree: 5

$\theta^4-2^{4} x\left(88\theta^4+32\theta^3+33\theta^2+17\theta+3\right)+2^{9} x^{2}\left(1504\theta^4+1408\theta^3+1436\theta^2+596\theta+93\right)-2^{18} x^{3}\left(776\theta^4+1344\theta^3+1381\theta^2+651\theta+117\right)+2^{23} 3 x^{4}(2\theta+1)(512\theta^3+1152\theta^2+1054\theta+339)-2^{31} 3^{2} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)$

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Coefficients of the holomorphic solution: 1, 48, 5328, 779520, 131619600, ...
--> OEIS
Normalized instanton numbers (n0=1): -80, -2954, -174096, -13270953, -1179175536, ... ; Common denominator:...

#### Discriminant

$-(128z-1)(384z-1)^2(256z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 384}$$\frac{ 1}{ 256}$$\frac{ 1}{ 128}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 2}$
$0$$1$$\frac{ 1}{ 2}$$1$$\frac{ 3}{ 4}$
$0$$3$$\frac{ 1}{ 2}$$1$$\frac{ 5}{ 4}$
$0$$4$$1$$2$$\frac{ 3}{ 2}$

#### Note:

This is operator "5.13" from ...

2

New Number: 7.2 |  AESZ:  |  Superseeker: -80 -249872  |  Hash: 341389ebf4ab0242c5b70d9a8fd7a1d9

Degree: 7

$\theta^4+2^{4} x\left(22\theta^4+64\theta^3+51\theta^2+19\theta+3\right)-2^{9} x^{2}\left(174\theta^4-624\theta^3-945\theta^2-417\theta-80\right)-2^{14} x^{3}\left(2230\theta^4+3000\theta^3-5121\theta^2-3813\theta-971\right)+2^{19} x^{4}\left(2860\theta^4-33320\theta^3+3363\theta^2+6847\theta+2402\right)+2^{27} x^{5}\left(7332\theta^4+480\theta^3+81\theta^2+1380\theta+719\right)+2^{36} 7 x^{6}(\theta+1)(46\theta^3+86\theta^2+67\theta+20)-2^{45} 7^{2} x^{7}\left((\theta+1)^4\right)$

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Coefficients of the holomorphic solution: 1, -48, 5072, -733440, 124117776, ...
--> OEIS
Normalized instanton numbers (n0=1): -80, -4202, -249872, -22251117, -2195810928, ... ; Common denominator:...

#### Discriminant

$-(64z+1)(32z-1)(224z-1)^2(256z+1)^3$

#### Local exponents

$-\frac{ 1}{ 64}$$-\frac{ 1}{ 256}$$0$$\frac{ 1}{ 224}$$\frac{ 1}{ 32}$$\infty$
$0$$0$$0$$0$$0$$1$
$1$$\frac{ 1}{ 2}$$0$$1$$1$$1$
$1$$\frac{ 3}{ 2}$$0$$3$$1$$1$
$2$$2$$0$$4$$2$$1$

#### Note:

This is operator "7.2" from ...