### Summary

You searched for: sol=360

1

New Number: 2.1 |  AESZ: 45  |  Superseeker: 12 3204  |  Hash: cdf289f6febf84eb577a238542a57457

Degree: 2

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

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Coefficients of the holomorphic solution: 1, 8, 360, 22400, 1695400, ...
--> OEIS
Normalized instanton numbers (n0=1): 12, 163, 3204, 107582, 4203360, ... ; Common denominator:...

#### Discriminant

$-(16z+1)(128z-1)$

#### Local exponents

$-\frac{ 1}{ 16}$$0$$\frac{ 1}{ 128}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$1$$0$$1$$\frac{ 1}{ 2}$
$1$$0$$1$$\frac{ 3}{ 2}$
$2$$0$$2$$\frac{ 3}{ 2}$

#### Note:

Hadamard product $A \ast a$, where $A$ is (:case 2.1.1)

2

New Number: 2.27 |  AESZ: 140  |  Superseeker: 108 -4945756  |  Hash: 74692097f8183c067c2c4b1a5c93387b

Degree: 2

$\theta^4-2^{2} 3 x(6\theta+1)(6\theta+5)(17\theta^2+17\theta+6)+2^{7} 3^{4} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)$

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Coefficients of the holomorphic solution: 1, 360, 582120, 1274232960, 3204505984680, ...
--> OEIS
Normalized instanton numbers (n0=1): 108, 54135, -4945756, 7925523138, -2434666062240, ... ; Common denominator:...

#### Discriminant

$(3888z-1)(3456z-1)$

#### Local exponents

$0$$\frac{ 1}{ 3888}$$\frac{ 1}{ 3456}$$\infty$
$0$$0$$0$$\frac{ 1}{ 6}$
$0$$1$$1$$\frac{ 5}{ 6}$
$0$$1$$1$$\frac{ 7}{ 6}$
$0$$2$$2$$\frac{ 11}{ 6}$

#### Note:

Hadamard product $D \ast g$

3

New Number: 5.88 |  AESZ: 324  |  Superseeker: 148/11 44108/11  |  Hash: 7f84d776cf00ff399b20865542185f87

Degree: 5

$11^{2} \theta^4-2^{2} 11 x\left(432\theta^4+624\theta^3+477\theta^2+165\theta+22\right)+2^{5} x^{2}\left(12944\theta^4+4736\theta^3-15491\theta^2-12914\theta-2860\right)-2^{4} 5 x^{3}\left(10688\theta^4-114048\theta^3-159132\theta^2-83028\theta-15455\right)-2^{11} 5^{2} x^{4}(2\theta+1)(4\theta+3)(76\theta^2+189\theta+125)+2^{14} 5^{3} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 360, 23120, 1796200, ...
--> OEIS
Normalized instanton numbers (n0=1): 148/11, 2044/11, 44108/11, 1459636/11, 60212712/11, ... ; Common denominator:...

#### Discriminant

$(5120z^3-512z^2-128z+1)(-11+160z)^2$

#### Local exponents

≈$-0.120643$$0$ ≈$0.007599$$\frac{ 11}{ 160}$ ≈$0.213044$$\infty$
$0$$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$0$$1$$1$$1$$\frac{ 3}{ 4}$
$1$$0$$1$$3$$1$$\frac{ 5}{ 4}$
$2$$0$$2$$4$$2$$\frac{ 3}{ 2}$

#### Note:

This is operator "5.88" from ...

4

New Number: 1.8 |  AESZ: 8  |  Superseeker: 2628 3966805740  |  Hash: 1a7187fdf63fe8761c969fdab1af1c36

Degree: 1

$\theta^4-2^{2} 3^{2} x(6\theta+1)(3\theta+1)(3\theta+2)(6\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 360, 1247400, 6861254400, 46381007673000, ...
--> OEIS
Normalized instanton numbers (n0=1): 2628, 2009484, 3966805740, 11533584001896, 41531678111043360, ... ; Common denominator:...

#### Discriminant

$1-11664z$

#### Local exponents

$0$$\frac{ 1}{ 11664}$$\infty$
$0$$0$$\frac{ 1}{ 6}$
$0$$1$$\frac{ 1}{ 3}$
$0$$1$$\frac{ 2}{ 3}$
$0$$2$$\frac{ 5}{ 6}$

#### Note:

A-incarnation of $X(6) \subset P^4(1,1,1,1,2)$.