### Summary

You searched for: sol=264

1

New Number: 5.110 |  AESZ: 377  |  Superseeker: 32/3 6752/3  |  Hash: 4b8e1b4341fae957e1766a0071de5ba5

Degree: 5

$3^{2} \theta^4-2^{3} 3 x\left(61\theta^4+74\theta^3+58\theta^2+21\theta+3\right)+2^{4} x^{2}\left(3883\theta^4+5356\theta^3+3451\theta^2+1278\theta+228\right)-2^{7} x^{3}\left(8067\theta^4+13410\theta^3+12875\theta^2+6336\theta+1236\right)+2^{14} x^{4}\left(413\theta^4+1069\theta^3+1206\theta^2+658\theta+140\right)-2^{19} 3 x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)$

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Coefficients of the holomorphic solution: 1, 8, 264, 13760, 873640, ...
--> OEIS
Normalized instanton numbers (n0=1): 32/3, 731/6, 6752/3, 355219/6, 5936896/3, ... ; Common denominator:...

#### Discriminant

$-(4z-1)(108z-1)(8z-1)(-3+64z)^2$

#### Local exponents

$0$$\frac{ 1}{ 108}$$\frac{ 3}{ 64}$$\frac{ 1}{ 8}$$\frac{ 1}{ 4}$$\infty$
$0$$0$$0$$0$$0$$\frac{ 2}{ 3}$
$0$$1$$1$$1$$1$$1$
$0$$1$$3$$1$$1$$1$
$0$$2$$4$$2$$2$$\frac{ 4}{ 3}$

#### Note:

This is operator "5.110" from ...

2

New Number: 5.24 |  AESZ: 195  |  Superseeker: 285/29 40626/29  |  Hash: 49a600431b3e9aaa9d9d6947f8df7d2b

Degree: 5

$29^{2} \theta^4-29 x\left(3026\theta^4+5848\theta^3+4577\theta^2+1653\theta+232\right)+x^{2}\left(5568+57768\theta+239159\theta^2+424220\theta^3+258647\theta^4\right)-x^{3}\left(76560+336864\theta+581647\theta^2+532614\theta^3+272743\theta^4\right)+2^{2} 17 x^{4}\left(1922\theta^4+6193\theta^3+8121\theta^2+4894\theta+1112\right)-2^{2} 3 17^{2} x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)$

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Coefficients of the holomorphic solution: 1, 8, 264, 13040, 778840, ...
--> OEIS
Normalized instanton numbers (n0=1): 285/29, 2362/29, 40626/29, 997476/29, 30096841/29, ... ; Common denominator:...

#### Discriminant

$-(27z^3-67z^2+102z-1)(-29+34z)^2$

#### Local exponents

$0$ ≈$0.009868$$\frac{ 29}{ 34}$ ≈$1.235807-1.492036I$ ≈$1.235807+1.492036I$$\infty$
$0$$0$$0$$0$$0$$\frac{ 2}{ 3}$
$0$$1$$1$$1$$1$$1$
$0$$1$$3$$1$$1$$1$
$0$$2$$4$$2$$2$$\frac{ 4}{ 3}$

#### Note:

This is operator "5.24" from ...

3

New Number: 14.1 |  AESZ:  |  Superseeker: 0 0  |  Hash: a8cf56492aecc07971e82c9104785180

Degree: 14

$\theta^4-x\left(13\theta^4+14\theta^3+16\theta^2+9\theta+2\right)+x^{2}\left(33\theta^4-88\theta^3-265\theta^2-324\theta-148\right)+x^{3}\left(217\theta^4+2362\theta^3+6403\theta^2+8178\theta+4160\right)-2 x^{4}\left(677\theta^4+4134\theta^3+8089\theta^2+6210\theta+360\right)+2^{2} 3 x^{5}\left(151\theta^4-1266\theta^3-11610\theta^2-28955\theta-25110\right)+2^{2} x^{6}\left(1895\theta^4+37302\theta^3+176991\theta^2+355848\theta+268836\right)-2^{2} x^{7}\left(9635\theta^4+89170\theta^3+185885\theta^2-107394\theta-522464\right)+2^{3} x^{8}\left(5907\theta^4-10636\theta^3-416125\theta^2-1666326\theta-2051920\right)+2^{5} x^{9}\left(2947\theta^4+80284\theta^3+519934\theta^2+1328475\theta+1205150\right)-2^{6} x^{10}\left(6122\theta^4+84852\theta^3+397555\theta^2+722745\theta+356430\right)+2^{6} 3 x^{11}\left(2259\theta^4+13398\theta^3-46549\theta^2-456244\theta-796656\right)+2^{7} 3^{2} x^{12}(\theta+4)(371\theta^3+8580\theta^2+53325\theta+101564)-2^{10} 3^{3} x^{13}(\theta+4)(\theta+5)(51\theta^2+519\theta+1330)+2^{11} 3^{4} 5 x^{14}(\theta+4)(\theta+5)^2(\theta+6)$

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Coefficients of the holomorphic solution: 1, 2, 16, 48, 264, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, 1/4, 0, -1/2, 0, ... ; Common denominator:...

#### Discriminant

$(z-1)(6z-1)(4z-1)(3z+1)(4z+1)(5z-1)(2z+1)^2(2z-1)^2(6z^2-2z+1)^2$

#### Local exponents

$-\frac{ 1}{ 2}$$-\frac{ 1}{ 3}$$-\frac{ 1}{ 4}$$0$$\frac{ 1}{ 6}-\frac{ 1}{ 6}\sqrt{ 5}I$$\frac{ 1}{ 6}$$\frac{ 1}{ 6}+\frac{ 1}{ 6}\sqrt{ 5}I$$\frac{ 1}{ 5}$$\frac{ 1}{ 4}$$\frac{ 1}{ 2}$$1$$\infty$
$0$$0$$0$$0$$0$$0$$0$$0$$0$$0$$0$$4$
$0$$1$$1$$0$$1$$1$$1$$1$$1$$0$$1$$5$
$-1$$1$$1$$0$$3$$1$$3$$1$$1$$-1$$1$$5$
$1$$2$$2$$0$$4$$2$$4$$2$$2$$1$$2$$6$

#### Note:

This is operator "14.1" from ...

4

New Number: 8.49 |  AESZ:  |  Superseeker: 56/3 17704/3  |  Hash: 4fa01cbee2fc74e3a62e00386e6fa1c0

Degree: 8

$3^{2} \theta^4-2^{2} 3 x\left(29\theta^4+178\theta^3+134\theta^2+45\theta+6\right)-2^{5} x^{2}\left(2233\theta^4+2536\theta^3+607\theta^2+132\theta+12\right)-2^{10} x^{3}\left(1274\theta^4+7425\theta^3+20002\theta^2+12717\theta+2670\right)+2^{13} x^{4}\left(2539\theta^4-36538\theta^3-52775\theta^2-31122\theta-6192\right)+2^{20} x^{5}\left(1617\theta^4+9771\theta^3+4484\theta^2-674\theta-556\right)+2^{25} x^{6}\left(1135\theta^4+4272\theta^3+3439\theta^2+858\theta+16\right)-2^{31} 3 x^{7}(2\theta+1)(110\theta^3+225\theta^2+184\theta+57)+2^{37} 3^{2} x^{8}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 264, 16640, 1130920, ...
--> OEIS
Normalized instanton numbers (n0=1): 56/3, -83/6, 17704/3, -25024/3, 13408832/3, ... ; Common denominator:...

#### Discriminant

$(4z-1)(131072z^3+2048z^2+88z-1)(48z+1)^2(64z-3)^2$

#### Local exponents

$-\frac{ 1}{ 48}$ ≈$-0.01214-0.027095I$ ≈$-0.01214+0.027095I$$0$ ≈$0.008655$$\frac{ 3}{ 64}$$\frac{ 1}{ 4}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$1$$1$$0$$1$$1$$1$$1$
$3$$1$$1$$0$$1$$3$$1$$1$
$4$$2$$2$$0$$2$$4$$2$$\frac{ 3}{ 2}$

#### Note:

This is operator "8.49" from ...