### Summary

You searched for: sol=468

1

New Number: 3.29 |  AESZ: 411  |  Superseeker: 3 237  |  Hash: 767c4e8d5a7bc53fbbd0d49797e65358

Degree: 3

$\theta^4-x\left(16+98\theta+235\theta^2+274\theta^3+145\theta^4\right)+2^{3} x^{2}(2\theta+1)(4\theta+5)(97\theta^2+190\theta+120)-2^{4} 3^{4} x^{3}(4\theta+5)(2\theta+3)(2\theta+1)(4\theta+9)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 468, 17520, 774060, ...
--> OEIS
Normalized instanton numbers (n0=1): 3, 36, 237, 4638, 72330, ... ; Common denominator:...

#### Discriminant

$-(81z-1)(-1+32z)^2$

#### Local exponents

$0$$\frac{ 1}{ 81}$$\frac{ 1}{ 32}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$0$$1$$\frac{ 1}{ 4}$$\frac{ 5}{ 4}$
$0$$1$$1$$\frac{ 3}{ 2}$
$0$$2$$\frac{ 5}{ 4}$$\frac{ 9}{ 4}$

#### Note:

This is operator "3.29" from ...

2

New Number: 5.44 |  AESZ: 240  |  Superseeker: 231/13 38037/13  |  Hash: 8f46cd6968b3b676e251a9d8635637fc

Degree: 5

$13^{2} \theta^4-13 x\left(1449\theta^4+4050\theta^3+3143\theta^2+1118\theta+156\right)-2^{4} x^{2}\left(22760\theta^4-27112\theta^3-121046\theta^2-82316\theta-17589\right)+2^{8} x^{3}\left(3824\theta^4+39936\theta^3-34292\theta^2-63492\theta-19539\right)-2^{16} 3 x^{4}(2\theta+1)(40\theta^3+684\theta^2+1013\theta+399)-2^{20} 3^{2} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 468, 28560, 2135700, ...
--> OEIS
Normalized instanton numbers (n0=1): 231/13, 826/13, 38037/13, 786076/13, 32662752/13, ... ; Common denominator:...

#### Discriminant

$-(128z-1)(128z^2-13z+1)(13+192z)^2$

#### Local exponents

$-\frac{ 13}{ 192}$$0$$\frac{ 1}{ 128}$$\frac{ 13}{ 256}-\frac{ 7}{ 256}\sqrt{ 7}I$$\frac{ 13}{ 256}+\frac{ 7}{ 256}\sqrt{ 7}I$$\infty$
$0$$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$0$$1$$1$$1$$\frac{ 3}{ 4}$
$3$$0$$1$$1$$1$$\frac{ 5}{ 4}$
$4$$0$$2$$2$$2$$\frac{ 3}{ 2}$

#### Note:

This is operator "5.44" from ...