### Summary

You searched for: h3=132

1

New Number: 2.64 |  AESZ: 182  |  Superseeker: 1 7  |  Hash: 89ba4729efa82413b33fe6928ff8d2c9

Degree: 2

$\theta^4-x\left(43\theta^4+86\theta^3+77\theta^2+34\theta+6\right)+2^{2} 3 x^{2}(\theta+1)^2(6\theta+5)(6\theta+7)$

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Coefficients of the holomorphic solution: 1, 6, 66, 924, 14850, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, 7/4, 7, 40, 270, ... ; Common denominator:...

#### Discriminant

$(27z-1)(16z-1)$

#### Local exponents

$0$$\frac{ 1}{ 27}$$\frac{ 1}{ 16}$$\infty$
$0$$0$$0$$\frac{ 5}{ 6}$
$0$$1$$1$$1$
$0$$1$$1$$1$
$0$$2$$2$$\frac{ 7}{ 6}$

#### Note:

This is operator "2.64" from ...

2

New Number: 5.25 |  AESZ: 198  |  Superseeker: -84/11 -9052/11  |  Hash: a1f924763b047c2720d99cfca5ca63db

Degree: 5

$11^{2} \theta^4+7 11 x\left(130\theta^4+266\theta^3+210\theta^2+77\theta+11\right)-x^{2}\left(11198+55253\theta+103725\theta^2+89990\theta^3+32126\theta^4\right)+x^{3}\left(1716+20625\theta+63474\theta^2+74184\theta^3+28723\theta^4\right)-7 x^{4}\left(1135\theta^4+2336\theta^3+1881\theta^2+713\theta+110\right)+7^{2} x^{5}\left((\theta+1)^4\right)$

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Coefficients of the holomorphic solution: 1, -7, 199, -8359, 423751, ...
--> OEIS
Normalized instanton numbers (n0=1): -84/11, 639/11, -9052/11, 189021/11, -4838013/11, ... ; Common denominator:...

#### Discriminant

$(z^3-159z^2+84z+1)(-11+7z)^2$

#### Local exponents

≈$-0.011648$$0$ ≈$0.541757$$\frac{ 11}{ 7}$ ≈$158.469891$$\infty$
$0$$0$$0$$0$$0$$1$
$1$$0$$1$$1$$1$$1$
$1$$0$$1$$3$$1$$1$
$2$$0$$2$$4$$2$$1$

#### Note:

There is a second MUM-point at infinity, corresponding to Operator AESZ 193/5.22

3

New Number: 5.79 |  AESZ: 310  |  Superseeker: 181/11 47171/11  |  Hash: 2b9b103b1c8f0d3175cd1fb9ef5aacc2

Degree: 5

$11^{2} \theta^4-11 x\left(1673\theta^4+3046\theta^3+2337\theta^2+814\theta+110\right)+2 5 x^{2}\left(19247\theta^4+28298\theta^3+13285\theta^2+3454\theta+660\right)-2^{2} x^{3}\left(167497\theta^4+245982\theta^3+227451\theta^2+115434\theta+22968\right)+2^{3} 5^{2} x^{4}\left(4079\theta^4+10270\theta^3+11427\theta^2+6226\theta+1340\right)-2^{5} 5^{4} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)$

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Coefficients of the holomorphic solution: 1, 10, 450, 30772, 2551810, ...
--> OEIS
Normalized instanton numbers (n0=1): 181/11, 2018/11, 47171/11, 3261479/22, 69313270/11, ... ; Common denominator:...

#### Discriminant

$-(z-1)(128z^2-142z+1)(-11+50z)^2$

#### Local exponents

$0$$\frac{ 71}{ 128}-\frac{ 17}{ 128}\sqrt{ 17}$$\frac{ 11}{ 50}$$1$$\frac{ 71}{ 128}+\frac{ 17}{ 128}\sqrt{ 17}$$\infty$
$0$$0$$0$$0$$0$$\frac{ 3}{ 4}$
$0$$1$$1$$1$$1$$1$
$0$$1$$3$$1$$1$$1$
$0$$2$$4$$2$$2$$\frac{ 5}{ 4}$

#### Note:

This is operator "5.79" from ...