### Summary

You searched for: c2h=68

1

New Number: 2.5 |  AESZ: 25  |  Superseeker: 20 8220  |  Hash: 93279abcbeeade30c29508de7784e582

Degree: 2

$\theta^4-2^{2} x(2\theta+1)^2(11\theta^2+11\theta+3)-2^{4} x^{2}(2\theta+1)^2(2\theta+3)^2$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 684, 58800, 6129900, ...
--> OEIS
Normalized instanton numbers (n0=1): 20, 277, 8220, 352994, 18651536, ... ; Common denominator:...

#### Discriminant

$1-176z-256z^2$

#### Local exponents

$-\frac{ 11}{ 32}-\frac{ 5}{ 32}\sqrt{ 5}$$0$$-\frac{ 11}{ 32}+\frac{ 5}{ 32}\sqrt{ 5}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$1$$0$$1$$\frac{ 1}{ 2}$
$1$$0$$1$$\frac{ 3}{ 2}$
$2$$0$$2$$\frac{ 3}{ 2}$

#### Note:

Hadamard product $A\ast b$

A-incarnation: X(1,2,2) in G(2,5)

2

New Number: 4.42 |  AESZ: 222  |  Superseeker: 69/5 29081/5  |  Hash: aad7a72e711c9c463396d319e0bf7603

Degree: 4

$5^{2} \theta^4-5 x\left(407\theta^4+1198\theta^3+909\theta^2+310\theta+40\right)-2^{7} x^{2}\left(2103\theta^4+6999\theta^3+8358\theta^2+4050\theta+680\right)-2^{12} x^{3}\left(1387\theta^4+3840\theta^3+3081\theta^2+960\theta+100\right)-2^{21} x^{4}\left((2\theta+1)^4\right)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 504, 36800, 3518200, ...
--> OEIS
Normalized instanton numbers (n0=1): 69/5, 1383/4, 29081/5, 346080, 72023607/5, ... ; Common denominator:...

#### Discriminant

$-(8192z^2+107z-1)(5+64z)^2$

#### Local exponents

$-\frac{ 5}{ 64}$$-\frac{ 107}{ 16384}-\frac{ 51}{ 16384}\sqrt{ 17}$$0$$s_1$$s_2$$-\frac{ 107}{ 16384}+\frac{ 51}{ 16384}\sqrt{ 17}$$\infty$
$0$$0$$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$1$$0$$1$$1$$1$$\frac{ 1}{ 2}$
$3$$1$$0$$1$$1$$1$$\frac{ 1}{ 2}$
$4$$2$$0$$2$$2$$2$$\frac{ 1}{ 2}$

#### Note:

Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ225/4.43

3

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 ...