### Summary

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

1

New Number: 4.47 |  AESZ: 239  |  Superseeker: 1584 171534960  |  Hash: 8e610c3437d7f38e552038bc55399495

Degree: 4

$\theta^4+2^{4} 3 x\left(9\theta^4-198\theta^3-131\theta^2-32\theta-3\right)-2^{11} 3^{2} x^{2}\left(486\theta^4+1215\theta^3+81\theta^2-27\theta-5\right)-2^{16} 3^{5} x^{3}\left(891\theta^4+972\theta^3+675\theta^2+216\theta+25\right)-2^{23} 3^{8} x^{4}(3\theta+1)^2(3\theta+2)^2$

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Coefficients of the holomorphic solution: 1, 144, 147600, 239904000, 479672701200, ...
--> OEIS
Normalized instanton numbers (n0=1): 1584, -17874, 171534960, 30012731550, 105934107802896, ... ; Common denominator:...

#### Discriminant

$-(432z+1)(3456z-1)(1+1728z)^2$

#### Local exponents

$-\frac{ 1}{ 432}$$-\frac{ 1}{ 1728}$$0$$\frac{ 1}{ 3456}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 3}$
$1$$1$$0$$1$$\frac{ 1}{ 3}$
$1$$3$$0$$1$$\frac{ 2}{ 3}$
$2$$4$$0$$2$$\frac{ 2}{ 3}$

#### Note:

2

New Number: 4.68 |  AESZ: 337  |  Superseeker: 2043/5 88982631/5  |  Hash: dc26e94a7c1daba6f627be36c42019b7

Degree: 4

$5^{2} \theta^4-3 5 x\left(3483\theta^4+6102\theta^3+4241\theta^2+1190\theta+120\right)+2^{5} 3^{2} x^{2}\left(31428\theta^4+35559\theta^3+243\theta^2-4320\theta-740\right)-2^{8} 3^{5} x^{3}\left(7371\theta^4+4860\theta^3+2997\theta^2+1080\theta+140\right)+2^{13} 3^{8} x^{4}(3\theta+1)^2(3\theta+2)^2$

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Coefficients of the holomorphic solution: 1, 72, 41400, 37396800, 41397463800, ...
--> OEIS
Normalized instanton numbers (n0=1): 2043/5, 279018/5, 88982631/5, 8604708876, 25774859896713/5, ... ; Common denominator:...

#### Discriminant

$(23328z^2-1917z+1)(-5+432z)^2$

#### Local exponents

$0$$s_1$$s_2$$\frac{ 71}{ 1728}-\frac{ 17}{ 1728}\sqrt{ 17}$$\frac{ 5}{ 432}$$\frac{ 71}{ 1728}+\frac{ 17}{ 1728}\sqrt{ 17}$$\infty$
$0$$0$$0$$0$$0$$0$$\frac{ 1}{ 3}$
$0$$1$$1$$1$$1$$1$$\frac{ 1}{ 3}$
$0$$1$$1$$1$$3$$1$$\frac{ 2}{ 3}$
$0$$2$$2$$2$$4$$2$$\frac{ 2}{ 3}$

#### Note:

3

New Number: 1.4 |  AESZ: 4  |  Superseeker: 117 713814  |  Hash: 1f2a9672b7cdc68eae658b2304b40dbd

Degree: 1

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

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Coefficients of the holomorphic solution: 1, 36, 8100, 2822400, 1200622500, ...
--> OEIS
Normalized instanton numbers (n0=1): 117, 5868, 713814, 126605376, 27754210287, ... ; Common denominator:...

#### Discriminant

$1-729z$

#### Local exponents

$0$$\frac{ 1}{ 729}$$\infty$
$0$$0$$\frac{ 1}{ 3}$
$0$$1$$\frac{ 1}{ 3}$
$0$$1$$\frac{ 2}{ 3}$
$0$$2$$\frac{ 2}{ 3}$

#### Note:

A-incarnation: X(3,3) in P^5.