### Summary

You searched for: inst=19

1

New Number: 3.20 |  AESZ: 390  |  Superseeker: 19 4455  |  Hash: cd8ca8746f3610e70893770a090533f9

Degree: 3

$\theta^4-x\left(561\theta^4+1122\theta^3+975\theta^2+414\theta+70\right)+2^{2} 7^{2} x^{2}(\theta+1)^2(534\theta^2+1068\theta+433)-2^{2} 7^{4} 13^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

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Coefficients of the holomorphic solution: 1, 70, 8442, 1192660, 182057050, ...
--> OEIS
Normalized instanton numbers (n0=1): 19, -276, 4455, -104648, 2969383, ... ; Common denominator:...

#### Discriminant

$-(169z-1)(-1+196z)^2$

#### Local exponents

$0$$\frac{ 1}{ 196}$$\frac{ 1}{ 169}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$0$$\frac{ 1}{ 6}$$1$$1$
$0$$\frac{ 5}{ 6}$$1$$2$
$0$$1$$2$$\frac{ 5}{ 2}$

#### Note:

This is operator "3.20" from ...

2

New Number: 5.122 |  AESZ:  |  Superseeker: 19 18641/3  |  Hash: 7cc1a0411f21ffd93f1a9f6468627432

Degree: 5

$\theta^4+x\left(119\theta^4-194\theta^3-143\theta^2-46\theta-6\right)-2^{2} 3^{2} x^{2}\left(46\theta^4+748\theta^3+379\theta^2+150\theta+27\right)-2^{2} 3^{4} x^{3}\left(2164\theta^4+6264\theta^3+7421\theta^2+4131\theta+846\right)-2^{5} 3^{8} x^{4}(2\theta+1)(76\theta^3+222\theta^2+235\theta+85)-2^{8} 3^{12} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

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Coefficients of the holomorphic solution: 1, 6, 162, 7620, 334530, ...
--> OEIS
Normalized instanton numbers (n0=1): 19, -170, 18641/3, -163734, 6446745, ... ; Common denominator:...

#### Discriminant

$-(81z-1)(1296z^2+56z+1)(1+72z)^2$

#### Local exponents

$-\frac{ 7}{ 324}-\frac{ 1}{ 81}\sqrt{ 2}I$$-\frac{ 7}{ 324}+\frac{ 1}{ 81}\sqrt{ 2}I$$-\frac{ 1}{ 72}$$0$$\frac{ 1}{ 81}$$\infty$
$0$$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$1$$1$$0$$1$$1$
$1$$1$$3$$0$$1$$1$
$2$$2$$4$$0$$2$$\frac{ 3}{ 2}$

#### Note:

B-Incarnation as fibre product 62211- 623--1

3

New Number: 6.12 |  AESZ:  |  Superseeker: 19 2263  |  Hash: 86993fb7955dee498aab7e103a0f457e

Degree: 6

$\theta^4-x\left(33\theta^4+258\theta^3+199\theta^2+70\theta+10\right)-2^{2} x^{2}\left(1380\theta^4+2400\theta^3-173\theta^2-634\theta-185\right)-2^{4} x^{3}\left(7325\theta^4+2670\theta^3-668\theta^2-1035\theta-290\right)-2^{7} x^{4}\left(897\theta^4-3504\theta^3-10058\theta^2-8492\theta-2435\right)+2^{12} x^{5}(\theta+1)^2(858\theta^2+1566\theta+745)-2^{17} 5^{2} x^{6}(\theta+1)^2(\theta+2)^2$

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Coefficients of the holomorphic solution: 1, 10, 310, 14860, 869590, ...
--> OEIS
Normalized instanton numbers (n0=1): 19, -18, 2263, 4184, 1097345, ... ; Common denominator:...

#### Discriminant

$-(z-1)(8z+1)(100z-1)(4z-1)(1+32z)^2$

#### Local exponents

$-\frac{ 1}{ 8}$$-\frac{ 1}{ 32}$$0$$\frac{ 1}{ 100}$$\frac{ 1}{ 4}$$1$$\infty$
$0$$0$$0$$0$$0$$0$$1$
$1$$1$$0$$1$$1$$1$$1$
$1$$3$$0$$1$$1$$1$$2$
$2$$4$$0$$2$$2$$2$$2$

#### Note:

This is operator "6.12" from ...