### Summary

You searched for: sol=-18

1

New Number: 3.7 |  AESZ: ~73  |  Superseeker: 90 151648  |  Hash: 9f672e1168859bdcc8ddc7a201c57968

Degree: 3

$\theta^4-2 3^{2} x\left(6\theta^4+12\theta^3+3\theta^2-3\theta-1\right)-2^{2} 3^{6} x^{2}(\theta+1)^2(20\theta^2+40\theta+17)-2^{4} 3^{10} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

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Coefficients of the holomorphic solution: 1, -18, 2754, 37620, 43789410, ...
--> OEIS
Normalized instanton numbers (n0=1): 90, 2196, 151648, 14813388, 1820806056, ... ; Common denominator:...

#### Discriminant

$-(324z-1)(1+108z)^2$

#### Local exponents

$-\frac{ 1}{ 108}$$0$$\frac{ 1}{ 324}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$0$$0$$1$$1$
$1$$0$$1$$2$
$1$$0$$2$$\frac{ 5}{ 2}$

#### Note:

Operator equivalent to AESZ 73

2

New Number: 12.14 |  AESZ:  |  Superseeker: 7/2 237/2  |  Hash: 614b95fc4275078df0800c7546870e7f

Degree: 12

$2^{2} \theta^4+2 x\left(74\theta^4+22\theta^3+77\theta^2+66\theta+18\right)+3^{2} x^{2}\left(97\theta^4+1206\theta^3+2235\theta^2+1750\theta+642\right)+3^{4} x^{3}\left(126\theta^4+3910\theta^3+7341\theta^2+8588\theta+3750\right)+3^{6} x^{4}\left(832\theta^4+6078\theta^3+26372\theta^2+37719\theta+21825\right)+3^{8} x^{5}\left(442\theta^4+12544\theta^3+62654\theta^2+116087\theta+78828\right)-3^{10} x^{6}\left(1032\theta^4-5126\theta^3-73629\theta^2-192529\theta-165306\right)-2 3^{12} x^{7}\left(1432\theta^4+11737\theta^3+11907\theta^2-41634\theta-71496\right)-3^{14} x^{8}\left(1871\theta^4+35422\theta^3+145979\theta^2+220752\theta+99504\right)+2 3^{17} x^{9}\left(151\theta^4-2094\theta^3-20341\theta^2-54972\theta-48672\right)+2^{3} 3^{19} x^{10}(\theta+3)(86\theta^3+414\theta^2+181\theta-936)+2^{3} 3^{22} x^{11}(\theta+4)(\theta+3)(21\theta^2+137\theta+224)+2^{4} 3^{24} x^{12}(\theta+3)(\theta+5)(\theta+4)^2$

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Coefficients of the holomorphic solution: 1, -9, -18, 747, -5751, ...
--> OEIS
Normalized instanton numbers (n0=1): 7/2, -193/8, 237/2, -6119/4, 16307, ... ; Common denominator:...

#### Discriminant

$(9z+1)(z+1)(324z^2-18z+1)(81z^2+9z+1)^2(486z^2-27z-2)^2$

#### Local exponents

$-1$$-\frac{ 1}{ 9}$$-\frac{ 1}{ 18}-\frac{ 1}{ 18}\sqrt{ 3}I$$-\frac{ 1}{ 18}+\frac{ 1}{ 18}\sqrt{ 3}I$$\frac{ 1}{ 36}-\frac{ 1}{ 108}\sqrt{ 57}$$0$$\frac{ 1}{ 36}-\frac{ 1}{ 36}\sqrt{ 3}I$$\frac{ 1}{ 36}+\frac{ 1}{ 36}\sqrt{ 3}I$$\frac{ 1}{ 36}+\frac{ 1}{ 108}\sqrt{ 57}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$0$$0$$3$
$1$$1$$0$$0$$1$$0$$1$$1$$1$$4$
$1$$1$$-1$$-1$$3$$0$$1$$1$$3$$4$
$2$$2$$1$$1$$4$$0$$2$$2$$4$$5$

#### Note:

This is operator "12.14" from ...

3

New Number: 9.7 |  AESZ:  |  Superseeker: 9 2564/3  |  Hash: 9bb7a7f3a3d5f66018396173696c194c

Degree: 9

$\theta^4+3 x\left(93\theta^4+42\theta^3+49\theta^2+28\theta+6\right)+2^{2} 3^{3} x^{2}\left(307\theta^4+328\theta^3+401\theta^2+230\theta+53\right)+2^{2} 3^{5} x^{3}\left(2268\theta^4+4128\theta^3+5443\theta^2+3525\theta+932\right)+2^{4} 3^{7} x^{4}\left(2588\theta^4+6880\theta^3+10145\theta^2+7398\theta+2167\right)+2^{6} 3^{9} x^{5}\left(1897\theta^4+6694\theta^3+11167\theta^2+9015\theta+2853\right)+2^{8} 3^{11} x^{6}\left(895\theta^4+3912\theta^3+7309\theta^2+6408\theta+2150\right)+2^{8} 3^{13} x^{7}\left(1048\theta^4+5360\theta^3+10939\theta^2+10155\theta+3534\right)+2^{10} 3^{15} x^{8}(\theta+1)(172\theta^3+804\theta^2+1295\theta+699)+2^{12} 3^{18} x^{9}(\theta+2)(\theta+1)(2\theta+3)^2$

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Coefficients of the holomorphic solution: 1, -18, 378, -8676, 213354, ...
--> OEIS
Normalized instanton numbers (n0=1): 9, -72, 2564/3, -12924, 228024, ... ; Common denominator:...

#### Discriminant

$(27z+1)(432z^2+36z+1)(36z+1)^2(648z^2+72z+1)^2$

#### Local exponents

$-\frac{ 1}{ 18}-\frac{ 1}{ 36}\sqrt{ 2}$$-\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I$$-\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I$$-\frac{ 1}{ 27}$$-\frac{ 1}{ 36}$$-\frac{ 1}{ 18}+\frac{ 1}{ 36}\sqrt{ 2}$$0$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$1$$1$$\frac{ 1}{ 2}$$1$$0$$\frac{ 3}{ 2}$
$3$$1$$1$$1$$\frac{ 1}{ 2}$$3$$0$$\frac{ 3}{ 2}$
$4$$2$$2$$2$$1$$4$$0$$2$

#### Note:

This is operator "9.7" from ...