### Summary

You searched for: sol=120

1

New Number: 2.4 |  AESZ: 62  |  Superseeker: 372 71562236  |  Hash: 07a3fd7577f878056e765831c6820f3d

Degree: 2

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

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Coefficients of the holomorphic solution: 1, 120, 138600, 228708480, 463140798120, ...
--> OEIS
Normalized instanton numbers (n0=1): 372, 136182, 71562236, 63364481358, 65860679690400, ... ; Common denominator:...

#### Discriminant

$-(432z+1)(3456z-1)$

#### Local exponents

$-\frac{ 1}{ 432}$$0$$\frac{ 1}{ 3456}$$\infty$
$0$$0$$0$$\frac{ 1}{ 6}$
$1$$0$$1$$\frac{ 5}{ 6}$
$1$$0$$1$$\frac{ 7}{ 6}$
$2$$0$$2$$\frac{ 11}{ 6}$

#### Note:

2

New Number: 2.69 |  AESZ: 205  |  Superseeker: 1 5  |  Hash: 4fb2e7002e630237d0458c3985cd6a18

Degree: 2

$\theta^4-x\left(59\theta^4+118\theta^3+105\theta^2+46\theta+8\right)+2^{5} 3 x^{2}(\theta+1)^2(3\theta+2)(3\theta+4)$

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Coefficients of the holomorphic solution: 1, 8, 120, 2240, 46840, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, 7/4, 5, 24, 759/5, ... ; Common denominator:...

#### Discriminant

$(32z-1)(27z-1)$

#### Local exponents

$0$$\frac{ 1}{ 32}$$\frac{ 1}{ 27}$$\infty$
$0$$0$$0$$\frac{ 2}{ 3}$
$0$$1$$1$$1$
$0$$1$$1$$1$
$0$$2$$2$$\frac{ 4}{ 3}$

#### Note:

This is operator "2.69" from ...

3

New Number: 5.107 |  AESZ: 364  |  Superseeker: 11/5 71/5  |  Hash: c5b4bc60bc9d39ea420bd49fad182557

Degree: 5

$5^{2} \theta^4-5 x\left(553\theta^4+722\theta^3+611\theta^2+250\theta+40\right)+2^{6} x^{2}\left(1914\theta^4+4722\theta^3+5519\theta^2+3010\theta+610\right)-2^{12} x^{3}\left(685\theta^4+2400\theta^3+3466\theta^2+2220\theta+500\right)+2^{19} x^{4}(2\theta+1)(30\theta^3+105\theta^2+122\theta+46)-2^{25} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

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Coefficients of the holomorphic solution: 1, 8, 120, 2240, 50680, ...
--> OEIS
Normalized instanton numbers (n0=1): 11/5, -8/5, 71/5, 738, 26841/5, ... ; Common denominator:...

#### Discriminant

$-(32768z^3-2560z^2+85z-1)(-5+64z)^2$

#### Local exponents

$0$ ≈$0.023029$ ≈$0.027548-0.023797I$ ≈$0.027548+0.023797I$$\frac{ 5}{ 64}$$\infty$
$0$$0$$0$$0$$0$$\frac{ 1}{ 2}$
$0$$1$$1$$1$$1$$1$
$0$$1$$1$$1$$3$$1$
$0$$2$$2$$2$$4$$\frac{ 3}{ 2}$

#### Note:

This is operator "5.107" from ...

4

New Number: 5.8 |  AESZ:  |  Superseeker: 84 1522388/3  |  Hash: f4b2a154823e983e64682b48f6254a15

Degree: 5

$\theta^4-2^{2} 3 x\left(192\theta^4+240\theta^3+191\theta^2+71\theta+10\right)+2^{7} 3^{2} x^{2}\left(1746\theta^4+3960\theta^3+4323\theta^2+2247\theta+395\right)-2^{12} 3^{4} x^{3}\left(2538\theta^4+7776\theta^3+9915\theta^2+5643\theta+1030\right)+2^{17} 3^{6} x^{4}\left(1782\theta^4+6480\theta^3+8793\theta^2+4905\theta+875\right)-2^{23} 3^{11} x^{5}(\theta+1)^2(3\theta+1)(3\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 120, 34920, 13157760, 5790070440, ...
--> OEIS
Normalized instanton numbers (n0=1): 84, 9210, 1522388/3, 120348978, 19186016160, ... ; Common denominator:...

#### Discriminant

$-(-1+864z)(432z-1)^2(288z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 864}$$\frac{ 1}{ 432}$$\frac{ 1}{ 288}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 3}$
$0$$1$$\frac{ 1}{ 6}$$1$$1$
$0$$1$$\frac{ 5}{ 6}$$3$$1$
$0$$2$$1$$4$$\frac{ 5}{ 3}$

#### Note:

This is operator "5.8" from ...

5

New Number: 8.55 |  AESZ:  |  Superseeker: 1 68/9  |  Hash: 39ed8ce7572bc79a333f77c892033bcf

Degree: 8

$\theta^4-x\left(33\theta^4+98\theta^3+105\theta^2+56\theta+12\right)+2^{3} x^{2}\left(34\theta^4+276\theta^3+609\theta^2+582\theta+216\right)+2^{4} 3 x^{3}\left(11\theta^4-170\theta^3-941\theta^2-1520\theta-846\right)-2^{7} 3^{2} x^{4}(2\theta^2+6\theta+5)(4\theta^2+12\theta-31)+2^{8} 3 x^{5}\left(11\theta^4+302\theta^3+1183\theta^2+1652\theta+726\right)+2^{11} x^{6}\left(34\theta^4+132\theta^3-39\theta^2-708\theta-747\right)-2^{12} x^{7}\left(33\theta^4+298\theta^3+1005\theta^2+1492\theta+816\right)+2^{16} x^{8}\left((\theta+3)^4\right)$

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Coefficients of the holomorphic solution: 1, 12, 120, 1216, 13080, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, -2, 68/9, -30, 150, ... ; Common denominator:...

#### Discriminant

$(z-1)(16z-1)(16z^2-16z+1)(4z-1)^2(4z+1)^2$

#### Local exponents

$-\frac{ 1}{ 4}$$0$$\frac{ 1}{ 16}$$\frac{ 1}{ 2}-\frac{ 1}{ 4}\sqrt{ 3}$$\frac{ 1}{ 4}$$\frac{ 1}{ 2}+\frac{ 1}{ 4}\sqrt{ 3}$$1$$\infty$
$0$$0$$0$$0$$0$$0$$0$$3$
$1$$0$$1$$1$$0$$1$$1$$3$
$3$$0$$1$$1$$-1$$1$$1$$3$
$4$$0$$2$$2$$1$$2$$2$$3$

#### Note:

This is operator "8.55" from ...

6

New Number: 1.1 |  AESZ: 1  |  Superseeker: 575 63441275  |  Hash: c86f1c284d8c5119801c6ba1343172bb

Degree: 1

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 120, 113400, 168168000, 305540235000, ...
--> OEIS
Normalized instanton numbers (n0=1): 575, 121850, 63441275, 48493506000, 45861177777525, ... ; Common denominator:...

#### Discriminant

$1-3125z$

#### Local exponents

$0$$\frac{ 1}{ 3125}$$\infty$
$0$$0$$\frac{ 1}{ 5}$
$0$$1$$\frac{ 2}{ 5}$
$0$$1$$\frac{ 3}{ 5}$
$0$$2$$\frac{ 4}{ 5}$

#### Note:

A-incarnation: $X(5) \subset P^4$
B-incarnation: mirror quintic.
P. Candelas, X. de la Ossa, D. Green, L. Parkes,{\em An exactly soluble superconformal theory from a mirror pair of Calabi-Yau manifolds}, Phys. Lett. B 258 (1991), no.1-2, 118-126.