### Summary

You searched for: inst=-33

1

New Number: 2.67 |  AESZ: 245  |  Superseeker: -6 -170  |  Hash: 0ef0bca0dbecbedad92696fd7c0f9e42

Degree: 2

$\theta^4-2 3 x\left(36\theta^4+66\theta^3+61\theta^2+28\theta+5\right)+2^{2} 3^{2} x^{2}(3\theta+2)^2(6\theta+7)^2$

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Coefficients of the holomorphic solution: 1, 30, 1764, 127776, 10248750, ...
--> OEIS
Normalized instanton numbers (n0=1): -6, -33, -170, -1029, -3246, ... ; Common denominator:...

#### Discriminant

$(108z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 108}$$\infty$
$0$$0$$\frac{ 2}{ 3}$
$0$$\frac{ 1}{ 6}$$\frac{ 2}{ 3}$
$0$$1$$\frac{ 7}{ 6}$
$0$$\frac{ 7}{ 6}$$\frac{ 7}{ 6}$

#### Note:

This is operator "2.67" from ...

2

New Number: 4.25 |  AESZ: 32  |  Superseeker: -33 -13051  |  Hash: bf53401dcbe0436fb67761f590ee3295

Degree: 4

$\theta^4-x\left(540\theta^4+1080\theta^3+1296\theta^2+756\theta+339/2\right)+x^{2}\left(72846\theta^4+291384\theta^3+881067/2\theta^2+298299\theta+305217/4\right)+x^{3}\left(14580\theta^4+87480\theta^3+209547\theta^2+234981\theta+205497/2\right)+x^{4}9/16(6\theta+11)^2(6\theta+13)^2$

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Coefficients of the holomorphic solution: 1, 339/2, 287415/8, 131845323/16, 251852894379/128, ...
--> OEIS
Normalized instanton numbers (n0=1): -33, -1995/4, -13051, -435975, -16838124, ... ; Common denominator:...

#### Discriminant

$(-1+270z+27z^2)^2$

#### Local exponents

$-5-\frac{ 26}{ 9}\sqrt{ 3}$$0$$s_1$$s_2$$-5+\frac{ 26}{ 9}\sqrt{ 3}$$\infty$
$0$$0$$-\frac{ 1}{ 2}$$-\frac{ 1}{ 2}$$0$$\frac{ 11}{ 6}$
$-\frac{ 1}{ 2}$$0$$0$$0$$-\frac{ 1}{ 2}$$\frac{ 11}{ 6}$
$1$$0$$1$$1$$1$$\frac{ 13}{ 6}$
$\frac{ 3}{ 2}$$0$$\frac{ 3}{ 2}$$\frac{ 3}{ 2}$$\frac{ 3}{ 2}$$\frac{ 13}{ 6}$

#### Note:

3

New Number: 4.9 |  AESZ:  |  Superseeker: -33 29693  |  Hash: c444fb1a912bd488ee5947b8bc1e2c53

Degree: 4

$\theta^4-x\left(756\theta^4+1512\theta^3+1824\theta^2+1068\theta+483/2\right)+x^{2}\left(260982\theta^4+1043928\theta^3+3947211/2\theta^2+1859355\theta+2817729/4\right)-x^{3}531441/2(2\theta+3)^2(42\theta^2+126\theta+127)+x^{4}387420489/16(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 483/2, 300015/8, 32162403/16, -132658029189/128, ...
--> OEIS
Normalized instanton numbers (n0=1): -33, 1095/2, 29693, 1241103/2, -16117818, ... ; Common denominator:...

#### Discriminant

$(1-378z+59049z^2)^2$

#### Local exponents

$0$$s_1$$s_2$$\frac{ 7}{ 2187}-\frac{ 4}{ 2187}\sqrt{ 2}I$$\frac{ 7}{ 2187}+\frac{ 4}{ 2187}\sqrt{ 2}I$$\infty$
$0$$-\frac{ 1}{ 2}$$-\frac{ 1}{ 2}$$0$$0$$\frac{ 3}{ 2}$
$0$$0$$0$$-\frac{ 1}{ 2}$$-\frac{ 1}{ 2}$$\frac{ 11}{ 6}$
$0$$1$$1$$1$$1$$\frac{ 13}{ 6}$
$0$$\frac{ 3}{ 2}$$\frac{ 3}{ 2}$$\frac{ 3}{ 2}$$\frac{ 3}{ 2}$$\frac{ 5}{ 2}$

#### Note:

YY-operator equivalent to AESZ 151=$B \ast \delta$