### Summary

You searched for: sol=1488

1

New Number: 2.35 |  AESZ: ~67  |  Superseeker: 480 -16034720  |  Hash: f06ee3928cd6d738db065f3f83d12160

Degree: 2

$\theta^4-2^{4} 3 x(2\theta+1)^2(72\theta^2+72\theta+31)+2^{12} 3^{6} x^{2}(2\theta+1)^2(2\theta+3)^2$

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Coefficients of the holomorphic solution: 1, 1488, 5351184, 24363091200, 123873273392400, ...
--> OEIS
Normalized instanton numbers (n0=1): 480, -226968, -16034720, 10943202744, -4352645747040, ... ; Common denominator:...

#### Discriminant

$(6912z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 6912}$$\infty$
$0$$0$$\frac{ 1}{ 2}$
$0$$\frac{ 1}{ 6}$$\frac{ 1}{ 2}$
$0$$\frac{ 5}{ 6}$$\frac{ 3}{ 2}$
$0$$1$$\frac{ 3}{ 2}$

#### Note:

This is operator "2.35" from ...

2

New Number: 4.53 |  AESZ: 264  |  Superseeker: 37216 464865119712  |  Hash: 625990ef22ba977bc3dd247ccc791780

Degree: 4

$\theta^4+2^{4} x\left(3392\theta^4-9344\theta^3-5764\theta^2-1092\theta-93\right)-2^{17} 3 x^{2}\left(1952\theta^4+15200\theta^3-7758\theta^2-2593\theta-323\right)-2^{26} 3^{2} 7 x^{3}\left(11584\theta^4-6912\theta^3-5364\theta^2-1632\theta-167\right)+2^{42} 3^{3} 7^{2} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)$

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Coefficients of the holomorphic solution: 1, 1488, 11258640, 139962144000, 2191135140810000, ...
--> OEIS
Normalized instanton numbers (n0=1): 37216, -75619080, 464865119712, -2749454414283384, 24030314100181942560, ... ; Common denominator:...

#### Discriminant

$(27648z-1)(4096z-1)(1+43008z)^2$

#### Local exponents

$-\frac{ 1}{ 43008}$$0$$\frac{ 1}{ 27648}$$\frac{ 1}{ 4096}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 3}$
$1$$0$$1$$1$$\frac{ 1}{ 2}$
$3$$0$$1$$1$$\frac{ 1}{ 2}$
$4$$0$$2$$2$$\frac{ 2}{ 3}$

#### Note:

3

New Number: 5.91 |  AESZ: 331  |  Superseeker: 112 186800  |  Hash: a30093d8c1ab2f66122cef8935b79efb

Degree: 5

$\theta^4+2^{4} x\left(18\theta^4-48\theta^3-33\theta^2-9\theta-1\right)-2^{9} x^{2}\left(86\theta^4+512\theta^3+125\theta^2+45\theta+10\right)-2^{14} x^{3}\left(1138\theta^4+2040\theta^3+1883\theta^2+879\theta+157\right)-2^{19} 7 x^{4}(2\theta+1)(186\theta^3+375\theta^2+317\theta+100)-2^{27} 7^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

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Coefficients of the holomorphic solution: 1, 16, 1488, 183040, 27611920, ...
--> OEIS
Normalized instanton numbers (n0=1): 112, -2242, 186800, -11675813, 1250599376, ... ; Common denominator:...

#### Discriminant

$-(32z+1)(256z-1)(64z+1)(1+224z)^2$

#### Local exponents

$-\frac{ 1}{ 32}$$-\frac{ 1}{ 64}$$-\frac{ 1}{ 224}$$0$$\frac{ 1}{ 256}$$\infty$
$0$$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:

This is operator "5.91" from ...