### Summary

You searched for: h3=24

1

New Number: 2.14 |  AESZ: 48  |  Superseeker: 24 5832  |  Hash: 8081a3989d09a7d612953dac3341d90c

Degree: 2

$\theta^4-2^{2} 3 x(3\theta+1)(3\theta+2)(3\theta^2+3\theta+1)+2^{5} 3^{2} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

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Coefficients of the holomorphic solution: 1, 24, 1800, 188160, 23423400, ...
--> OEIS
Normalized instanton numbers (n0=1): 24, 291/2, 5832, 247116, 12634944, ... ; Common denominator:...

#### Discriminant

$(216z-1)(108z-1)$

#### Local exponents

$0$$\frac{ 1}{ 216}$$\frac{ 1}{ 108}$$\infty$
$0$$0$$0$$\frac{ 1}{ 3}$
$0$$1$$1$$\frac{ 2}{ 3}$
$0$$1$$1$$\frac{ 4}{ 3}$
$0$$2$$2$$\frac{ 5}{ 3}$

#### Note:

B*d

2

New Number: 2.1 |  AESZ: 45  |  Superseeker: 12 3204  |  Hash: cdf289f6febf84eb577a238542a57457

Degree: 2

$\theta^4-2^{2} x(2\theta+1)^2(7\theta^2+7\theta+2)-2^{7} x^{2}(2\theta+1)^2(2\theta+3)^2$

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Coefficients of the holomorphic solution: 1, 8, 360, 22400, 1695400, ...
--> OEIS
Normalized instanton numbers (n0=1): 12, 163, 3204, 107582, 4203360, ... ; Common denominator:...

#### Discriminant

$-(16z+1)(128z-1)$

#### Local exponents

$-\frac{ 1}{ 16}$$0$$\frac{ 1}{ 128}$$\infty$
$0$$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 $A \ast a$, where $A$ is (:case 2.1.1)

3

New Number: 2.26 |  AESZ: 139  |  Superseeker: 44 22500  |  Hash: f5d9215987323abcff6ed8709927af5d

Degree: 2

$\theta^4-2^{2} x(4\theta+1)(4\theta+3)(17\theta^2+17\theta+6)+2^{7} 3^{2} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)$

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Coefficients of the holomorphic solution: 1, 72, 17640, 5765760, 2156754600, ...
--> OEIS
Normalized instanton numbers (n0=1): 44, 607, 22500, 1444678, 128626784, ... ; Common denominator:...

#### Discriminant

$(576z-1)(512z-1)$

#### Local exponents

$0$$\frac{ 1}{ 576}$$\frac{ 1}{ 512}$$\infty$
$0$$0$$0$$\frac{ 1}{ 4}$
$0$$1$$1$$\frac{ 3}{ 4}$
$0$$1$$1$$\frac{ 5}{ 4}$
$0$$2$$2$$\frac{ 7}{ 4}$

#### Note:

Hadamard product $C \ast g$

4

New Number: 2.53 |  AESZ: 29  |  Superseeker: 14 10424/3  |  Hash: 92e8a038051b3fb8e0cc6ad6a52b8bfb

Degree: 2

$\theta^4-2 x(2\theta+1)^2(17\theta^2+17\theta+5)+2^{2} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)$

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Coefficients of the holomorphic solution: 1, 10, 438, 28900, 2310070, ...
--> OEIS
Normalized instanton numbers (n0=1): 14, 303/2, 10424/3, 113664, 4579068, ... ; Common denominator:...

#### Discriminant

$1-136z+16z^2$

#### Local exponents

$0$$\frac{ 17}{ 4}-3\sqrt{ 2}$$\frac{ 17}{ 4}+3\sqrt{ 2}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$0$$1$$1$$1$
$0$$1$$1$$1$
$0$$2$$2$$\frac{ 3}{ 2}$

#### Note:

Hadamard product $I \ast \gamma$

5

New Number: 2.9 |  AESZ: 58  |  Superseeker: 16 11056/3  |  Hash: 1ca6d3d1c4514db0651efce420265f5a

Degree: 2

$\theta^4-2^{2} x(2\theta+1)^2(10\theta^2+10\theta+3)+2^{4} 3^{2} x^{2}(2\theta+1)^2(2\theta+3)^2$

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Coefficients of the holomorphic solution: 1, 12, 540, 37200, 3131100, ...
--> OEIS
Normalized instanton numbers (n0=1): 16, 142, 11056/3, 121470, 4971792, ... ; Common denominator:...

#### Discriminant

$(144z-1)(16z-1)$

#### Local exponents

$0$$\frac{ 1}{ 144}$$\frac{ 1}{ 16}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$0$$1$$1$$\frac{ 1}{ 2}$
$0$$1$$1$$\frac{ 3}{ 2}$
$0$$2$$2$$\frac{ 3}{ 2}$

#### Note:

6

New Number: 5.42 |  AESZ: 231  |  Superseeker: 460/3 894404/3  |  Hash: 6f793238336123adfdcd7ee17d64e5ec

Degree: 5

$3^{2} \theta^4-2^{2} 3 x\left(28\theta^4+1016\theta^3+739\theta^2+231\theta+30\right)-2^{9} x^{2}\left(1168\theta^4-968\theta^3-9518\theta^2-5325\theta-1005\right)+2^{16} x^{3}\left(988\theta^4+8208\theta^3-743\theta^2-4230\theta-1245\right)+2^{24} 5 x^{4}(2\theta+1)^2(9\theta^2-279\theta-277)-2^{33} 5^{2} x^{5}(2\theta+1)^2(2\theta+3)^2$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 40, 3240, 313600, 39327400, ...
--> OEIS
Normalized instanton numbers (n0=1): 460/3, -16828/3, 894404/3, -42271624/3, 2076730720/3, ... ; Common denominator:...

#### Discriminant

$-(256z-1)(32768z^2-208z+1)(3+640z)^2$

#### Local exponents

$-\frac{ 3}{ 640}$$0$$\frac{ 13}{ 4096}-\frac{ 7}{ 4096}\sqrt{ 7}I$$\frac{ 13}{ 4096}+\frac{ 7}{ 4096}\sqrt{ 7}I$$\frac{ 1}{ 256}$$\infty$
$0$$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$0$$1$$1$$1$$\frac{ 1}{ 2}$
$3$$0$$1$$1$$1$$\frac{ 3}{ 2}$
$4$$0$$2$$2$$2$$\frac{ 3}{ 2}$

#### Note:

This is operator "5.42" from ...