### Summary

You searched for: sol=126

1

New Number: 2.29 |  AESZ: 142  |  Superseeker: 45 27735  |  Hash: 85c2c2d8111a859d4cc03e8892c56af9

Degree: 2

$\theta^4-3^{2} x(3\theta+1)(3\theta+2)(18\theta^2+18\theta+7)+3^{8} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

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Coefficients of the holomorphic solution: 1, 126, 44550, 20447280, 10600093350, ...
--> OEIS
Normalized instanton numbers (n0=1): 45, -3465/4, 27735, -1156005, 55721970, ... ; Common denominator:...

#### Discriminant

$(729z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 729}$$\infty$
$0$$0$$\frac{ 1}{ 3}$
$0$$\frac{ 1}{ 3}$$\frac{ 2}{ 3}$
$0$$\frac{ 2}{ 3}$$\frac{ 4}{ 3}$
$0$$1$$\frac{ 5}{ 3}$

#### Note:

Hadamard product $A \ast$

2

New Number: 2.62 |  AESZ: 28  |  Superseeker: 5 312  |  Hash: 06dd455cafc5097e4f671d385984c1a2

Degree: 2

$\theta^4-x\left(65\theta^4+130\theta^3+105\theta^2+40\theta+6\right)+2^{2} x^{2}(4\theta+3)(\theta+1)^2(4\theta+5)$

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Coefficients of the holomorphic solution: 1, 6, 126, 3948, 149310, ...
--> OEIS
Normalized instanton numbers (n0=1): 5, 28, 312, 4808, 91048, ... ; Common denominator:...

#### Discriminant

$(64z-1)(z-1)$

#### Local exponents

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

#### Note:

A-incarnation: $X(1, 1, 1, 1, 1, 1) \subset Grass(3, 6)$

3

New Number: 11.13 |  AESZ:  |  Superseeker: 70/13 15323/39  |  Hash: 89df09ff1ec0d5dfcae0791579c9095e

Degree: 11

$13^{2} \theta^4-2 13 x\left(593\theta^4+850\theta^3+685\theta^2+260\theta+39\right)+2^{2} x^{2}\left(81227\theta^4+145178\theta^3+121774\theta^2+52312\theta+9477\right)-x^{3}\left(3180153\theta^4+8754414\theta^3+11733109\theta^2+7260552\theta+1687608\right)+2 x^{4}\left(9121117\theta^4+38823752\theta^3+61935546\theta^2+41745416\theta+10192764\right)-2^{2} x^{5}\left(14736265\theta^4+81359956\theta^3+152008790\theta^2+112521671\theta+29176827\right)+2^{2} 3^{2} x^{6}\left(1220244\theta^4+12211662\theta^3+31283769\theta^2+26817500\theta+7548762\right)+2^{2} 3^{2} x^{7}\left(4505067\theta^4+14797690\theta^3+6324743\theta^2-4986206\theta-2940402\right)-2^{3} 3^{3} x^{8}\left(855097\theta^4+3900198\theta^3+2679311\theta^2-619598\theta-662876\right)-2^{4} 3^{3} x^{9}\left(254021\theta^4+398518\theta^3+352691\theta^2+205022\theta+53940\right)+2^{5} 3^{3} 11 x^{10}\left(13283\theta^4+25990\theta^3+18039\theta^2+5062\theta+456\right)+2^{7} 3^{3} 11^{2} x^{11}(4\theta+3)(\theta+1)^2(4\theta+5)$

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Coefficients of the holomorphic solution: 1, 6, 126, 4092, 160110, ...
--> OEIS
Normalized instanton numbers (n0=1): 70/13, 420/13, 15323/39, 78225/13, 1564284/13, ... ; Common denominator:...

#### Discriminant

$(192z^2-69z+1)(2z^3+39z^2-5z+1)(13-112z-18z^2+132z^3)^2$

#### Local exponents

≈$-19.628663$ ≈$-0.912176$$0$$\frac{ 23}{ 128}-\frac{ 11}{ 384}\sqrt{ 33}$ ≈$0.064331-0.146063I$ ≈$0.064331+0.146063I$ ≈$0.115746$$\frac{ 23}{ 128}+\frac{ 11}{ 384}\sqrt{ 33}$ ≈$0.932793$$\infty$
$0$$0$$0$$0$$0$$0$$0$$0$$0$$\frac{ 3}{ 4}$
$1$$1$$0$$1$$1$$1$$1$$1$$1$$1$
$1$$3$$0$$1$$1$$1$$3$$1$$3$$1$
$2$$4$$0$$2$$2$$2$$4$$2$$4$$\frac{ 5}{ 4}$

#### Note:

This is operator "11.13" from ...