### Summary

You searched for: sol=2448

1

New Number: 2.43 |  AESZ: ~77, ~78,~97  |  Superseeker: -736 -26911072  |  Hash: 3d2cd06eccf32145816b35cb63878900

Degree: 2

$\theta^4-2^{4} x\left(512\theta^4+1024\theta^3+1208\theta^2+696\theta+153\right)+2^{12} x^{2}(8\theta+7)^2(8\theta+9)^2$

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Coefficients of the holomorphic solution: 1, 2448, 7779600, 26927622400, 97242114301200, ...
--> OEIS
Normalized instanton numbers (n0=1): -736, -104512, -26911072, -9061573696, -3547993303456, ... ; Common denominator:...

#### Discriminant

$(4096z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 4096}$$\infty$
$0$$0$$\frac{ 7}{ 8}$
$0$$-\frac{ 1}{ 2}$$\frac{ 7}{ 8}$
$0$$1$$\frac{ 9}{ 8}$
$0$$\frac{ 3}{ 2}$$\frac{ 9}{ 8}$

#### Note:

Operator equivalent to $\hat{6}$

2

New Number: 5.14 |  AESZ: 116  |  Superseeker: 64 23360  |  Hash: 0b366ad8c78b6697205c5a7fff270f5b

Degree: 5

$\theta^4-2^{5} x\left(10\theta^4+26\theta^3+20\theta^2+7\theta+1\right)+2^{8} x^{2}\left(52\theta^4+472\theta^3+832\theta^2+492\theta+103\right)+2^{16} x^{3}\left(14\theta^4+12\theta^3-96\theta^2-105\theta-29\right)-2^{18} x^{4}(2\theta+1)(56\theta^3+468\theta^2+646\theta+249)-2^{24} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)$

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Coefficients of the holomorphic solution: 1, 32, 2448, 273920, 38525200, ...
--> OEIS
Normalized instanton numbers (n0=1): 64, 12, 23360, 654490, 53956288, ... ; Common denominator:...

#### Discriminant

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

#### Local exponents

$-\frac{ 1}{ 32}$$0$$\frac{ 1}{ 256}$$\frac{ 1}{ 64}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$0$$1$$\frac{ 1}{ 2}$$\frac{ 3}{ 4}$
$3$$0$$1$$\frac{ 1}{ 2}$$\frac{ 5}{ 4}$
$4$$0$$2$$1$$\frac{ 3}{ 2}$

#### Note:

This is operator "5.14" from ...