### Summary

You searched for: superseeker=-12/5,136/3

Your search produced exactly one match

1

New Number: 8.39 |  AESZ:  |  Superseeker: -12/5 136/3  |  Hash: c1330764e09752f7bb8e86b15541c588

Degree: 8

$5^{2} \theta^4+2 3 5 x\left(51\theta^4+84\theta^3+72\theta^2+30\theta+5\right)+2^{2} 3 x^{2}\left(3297\theta^4+10236\theta^3+13562\theta^2+8110\theta+1830\right)+2^{2} 3^{3} x^{3}\left(3866\theta^4+14088\theta^3+21137\theta^2+14355\theta+3600\right)+2^{3} 3^{3} x^{4}\left(11680\theta^4+38792\theta^3+45641\theta^2+24205\theta+4854\right)+2^{4} 3^{5} x^{5}\left(2624\theta^4+8240\theta^3+8275\theta^2+2971\theta+216\right)+2^{5} 3^{5} x^{6}\left(3248\theta^4+8832\theta^3+9739\theta^2+4803\theta+882\right)+2^{7} 3^{7} x^{7}\left(144\theta^4+384\theta^3+428\theta^2+233\theta+51\right)+2^{9} 3^{7} x^{8}(4\theta+3)(\theta+1)^2(4\theta+5)$

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Coefficients of the holomorphic solution: 1, -6, 54, -348, -3690, ...
--> OEIS
Normalized instanton numbers (n0=1): -12/5, -21/5, 136/3, -1743/10, -1056/5, ... ; Common denominator:...

#### Discriminant

$(1+54z+1152z^2+6048z^3+3456z^4)(5+18z+72z^2)^2$

#### Local exponents

≈$-1.540068$ ≈$-0.152177$$-\frac{ 1}{ 8}-\frac{ 1}{ 24}\sqrt{ 31}I$$-\frac{ 1}{ 8}+\frac{ 1}{ 24}\sqrt{ 31}I$ ≈$-0.028878$ ≈$-0.028878$$0$$\infty$
$0$$0$$0$$0$$0$$0$$0$$\frac{ 3}{ 4}$
$1$$1$$1$$1$$1$$1$$0$$1$
$1$$1$$3$$3$$1$$1$$0$$1$
$2$$2$$4$$4$$2$$2$$0$$\frac{ 5}{ 4}$

#### Note:

This is operator "8.39" from ...

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