### Summary

You searched for: superseeker=12,3020/3

Your search produced exactly one match

1

New Number: 8.13 |  AESZ: 163  |  Superseeker: 12 3020/3  |  Hash: e21fd830a9dca03305deb8363a26fcf2

Degree: 8

$\theta^4-2^{2} 3 x\left((3\theta^2+3\theta+1)^2\right)+2^{4} 3^{2} x^{2}\left(21\theta^4+156\theta^3+219\theta^2+126\theta+29\right)+2^{7} 3^{4} x^{3}(3\theta^2+3\theta+1)(3\theta^2-21\theta-35)-2^{10} 3^{5} x^{4}\left(27\theta^4+54\theta^3-114\theta^2-141\theta-49\right)+2^{12} 3^{7} x^{5}(3\theta^2+3\theta+1)(3\theta^2+27\theta-11)+2^{14} 3^{8} x^{6}\left(21\theta^4-72\theta^3-123\theta^2-72\theta-13\right)-2^{17} 3^{10} x^{7}\left((3\theta^2+3\theta+1)^2\right)+2^{20} 3^{12} x^{8}\left((\theta+1)^4\right)$

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Coefficients of the holomorphic solution: 1, 12, 180, 2352, 6084, ...
--> OEIS
Normalized instanton numbers (n0=1): 12, -96, 3020/3, -71493/4, 319584, ... ; Common denominator:...

#### Discriminant

$(1728z^2-72z+1)(432z^2-36z+1)(-1+864z^2)^2$

#### Local exponents

$-\frac{ 1}{ 72}\sqrt{ 6}$$0$$\frac{ 1}{ 48}-\frac{ 1}{ 144}\sqrt{ 3}I$$\frac{ 1}{ 48}+\frac{ 1}{ 144}\sqrt{ 3}I$$\frac{ 1}{ 72}\sqrt{ 6}$$\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I$$\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$1$$0$$1$$1$$1$$1$$1$$1$
$3$$0$$1$$1$$3$$1$$1$$1$
$4$$0$$2$$2$$4$$2$$2$$1$

#### Note:

Hadamard product $d \ast f$. This operator has a second MUM-point at infinity with the same instanton numbers. Itg can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\sqrt{?})$.