### Summary

You searched for: sol=1224

Your search produced 2 matches

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1

New Number: 6.14 |  AESZ:  |  Superseeker: 8 9928/3  |  Hash: 44968de144621e2fa74ce3964a5435f7

Degree: 6

$\theta^4-2^{2} x(5\theta^2+5\theta+2)(13\theta^2+13\theta+3)+2^{5} x^{2}\left(533\theta^4+2132\theta^3+3137\theta^2+2010\theta+432\right)-2^{8} 3 x^{3}\left(652\theta^4+3912\theta^3+8229\theta^2+7083\theta+1845\right)+2^{12} 3^{2} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)-2^{15} 3^{3} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2+2^{17} 3^{4} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)$

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Coefficients of the holomorphic solution: 1, 24, 1224, 96000, 9633960, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, 471/2, 9928/3, 185385, 6071232, ... ; Common denominator:...

#### Discriminant

$(12z-1)(24z-1)(2304z^2-192z+1)(-1+16z)^2$

#### Local exponents

$0$$\frac{ 1}{ 24}-\frac{ 1}{ 48}\sqrt{ 3}$$\frac{ 1}{ 24}$$\frac{ 1}{ 16}$$\frac{ 1}{ 24}+\frac{ 1}{ 48}\sqrt{ 3}$$\frac{ 1}{ 12}$$\infty$
$0$$0$$0$$0$$0$$0$$\frac{ 1}{ 2}$
$0$$1$$1$$\frac{ 1}{ 2}$$1$$1$$\frac{ 5}{ 2}$
$0$$1$$1$$\frac{ 1}{ 2}$$1$$1$$\frac{ 7}{ 2}$
$0$$2$$2$$1$$2$$2$$\frac{ 11}{ 2}$

#### Note:

This is operator "6.14" from ...

2

New Number: 8.88 |  AESZ:  |  Superseeker: 571/15 394769/15  |  Hash: 96ea6b0b71373481f874100af7f89d67

Degree: 8

$3^{2} 5^{2} \theta^4-3 5 x\left(4063\theta^4+7682\theta^3+5731\theta^2+1890\theta+240\right)+2 x^{2}\left(605228\theta^4+1651274\theta^3+1743713\theta^2+827790\theta+149520\right)-2^{2} x^{3}\left(122453\theta^4+9232248\theta^3+20066474\theta^2+11895930\theta+2347980\right)-2^{3} x^{4}\left(14154736\theta^4-3374404\theta^3-69996921\theta^2-57156850\theta-13566428\right)+2^{4} x^{5}\left(30476536\theta^4+168961384\theta^3-11782973\theta^2-90041748\theta-28710648\right)+2^{6} 23 x^{6}\left(1194624\theta^4-7988712\theta^3-9497764\theta^2-3726021\theta-451296\right)-2^{8} 7 23^{2} x^{7}(2\theta+1)(8454\theta^3+5577\theta^2-4303\theta-3155)+2^{10} 7^{2} 23^{3} x^{8}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)$

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Coefficients of the holomorphic solution: 1, 16, 1224, 146320, 21334600, ...
--> OEIS
Normalized instanton numbers (n0=1): 571/15, 3038/5, 394769/15, 23541584/15, 352406944/3, ... ; Common denominator:...

#### Discriminant

$(1-261z+2952z^2-12368z^3+23552z^4)(-15+74z+1288z^2)^2$

#### Local exponents

$0$$s_1$$s_3$$s_2$$s_5$$s_4$$s_6$$\infty$
$0$$0$$0$$0$$0$$0$$0$$\frac{ 1}{ 2}$
$0$$1$$1$$1$$1$$1$$1$$\frac{ 3}{ 4}$
$0$$3$$1$$3$$1$$1$$1$$\frac{ 5}{ 4}$
$0$$4$$2$$4$$2$$2$$2$$\frac{ 3}{ 2}$

#### Note:

This is operator "8.88" from ...