### Summary

You searched for: Spectrum0=1/4,1/3,2/3,3/4

1

New Number: 4.60 |  AESZ: 288  |  Superseeker: 3616 264403872  |  Hash: 3373ebdbe30d220b5562cfd77d4e8f96

Degree: 4

$\theta^4-2^{4} x\left(496\theta^4+1568\theta^3+1060\theta^2+276\theta+27\right)-2^{15} 3 x^{2}\left(32\theta^4-760\theta^3-1570\theta^2-651\theta-81\right)+2^{22} 3^{2} x^{3}\left(1616\theta^4+6912\theta^3+5092\theta^2+1416\theta+135\right)+2^{34} 3^{3} x^{4}(4\theta+1)(3\theta+1)(3\theta+2)(4\theta+3)$

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Coefficients of the holomorphic solution: 1, 432, 982800, 3259872000, 12958462717200, ...
--> OEIS
Normalized instanton numbers (n0=1): 3616, 114144, 264403872, 424149521656, 710239010095456, ... ; Common denominator:...

#### Discriminant

$(6912z-1)(4096z-1)(1+1536z)^2$

#### Local exponents

$-\frac{ 1}{ 1536}$$0$$\frac{ 1}{ 6912}$$\frac{ 1}{ 4096}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 4}$
$1$$0$$1$$1$$\frac{ 1}{ 3}$
$3$$0$$1$$1$$\frac{ 2}{ 3}$
$4$$0$$2$$2$$\frac{ 3}{ 4}$

#### Note:

2

New Number: 1.11 |  AESZ: 11  |  Superseeker: 324 10792428  |  Hash: 8ac8b98b80383c9f0ea125ccd6e6a55d

Degree: 1

$\theta^4-2^{2} 3 x(4\theta+1)(3\theta+1)(3\theta+2)(4\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 72, 37800, 31046400, 31216185000, ...
--> OEIS
Normalized instanton numbers (n0=1): 324, 37260, 10792428, 4580482284, 2405245303584, ... ; Common denominator:...

#### Discriminant

$1-1728z$

#### Local exponents

$0$$\frac{ 1}{ 1728}$$\infty$
$0$$0$$\frac{ 1}{ 4}$
$0$$1$$\frac{ 1}{ 3}$
$0$$1$$\frac{ 2}{ 3}$
$0$$2$$\frac{ 3}{ 4}$

#### Note:

A-incarnation: X(4,6) in P^5(1,1,1,2,2,3)