### Summary

You searched for: inst=52

1

New Number: 2.3 |  AESZ: 68  |  Superseeker: 52 220220  |  Hash: 13a48045ff0a42a9fcfbdb710baf1997

Degree: 2

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

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Coefficients of the holomorphic solution: 1, 24, 4200, 1034880, 311711400, ...
--> OEIS
Normalized instanton numbers (n0=1): 52, 2814, 220220, 29135058, 4512922272, ... ; Common denominator:...

#### Discriminant

$-(64z+1)(512z-1)$

#### Local exponents

$-\frac{ 1}{ 64}$$0$$\frac{ 1}{ 512}$$\infty$
$0$$0$$0$$\frac{ 1}{ 4}$
$1$$0$$1$$\frac{ 3}{ 4}$
$1$$0$$1$$\frac{ 5}{ 4}$
$2$$0$$2$$\frac{ 7}{ 4}$

#### Note:

C*a

2

New Number: 3.1 |  AESZ: 34  |  Superseeker: 1 28/3  |  Hash: e5461c5f5ae4d929328f66b8955a31f5

Degree: 3

$\theta^4-x\left(35\theta^4+70\theta^3+63\theta^2+28\theta+5\right)+x^{2}(\theta+1)^2(259\theta^2+518\theta+285)-3^{2} 5^{2} x^{3}(\theta+1)^2(\theta+2)^2$

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Coefficients of the holomorphic solution: 1, 5, 45, 545, 7885, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, 2, 28/3, 52, 350, ... ; Common denominator:...

#### Discriminant

$-(z-1)(25z-1)(9z-1)$

#### Local exponents

$0$$\frac{ 1}{ 25}$$\frac{ 1}{ 9}$$1$$\infty$
$0$$0$$0$$0$$1$
$0$$1$$1$$1$$1$
$0$$1$$1$$1$$2$
$0$$2$$2$$2$$2$

3

New Number: 12.17 |  AESZ:  |  Superseeker: 4 52  |  Hash: e65be092d4832d3740d2a3078755f447

Degree: 12

$\theta^4+2^{2} x\left(24\theta^4+6\theta^3+11\theta^2+8\theta+2\right)+2^{4} x^{2}\left(209\theta^4+2\theta^3+23\theta^2-10\right)+2^{7} x^{3}\left(223\theta^4-1218\theta^3-2225\theta^2-2088\theta-776\right)-2^{10} x^{4}\left(1409\theta^4+9634\theta^3+19337\theta^2+18420\theta+6872\right)-2^{13} x^{5}\left(6527\theta^4+35858\theta^3+78357\theta^2+78428\theta+30414\right)-2^{17} x^{6}\left(6276\theta^4+37704\theta^3+91143\theta^2+97914\theta+40036\right)-2^{21} x^{7}\left(2923\theta^4+22130\theta^3+61939\theta^2+73401\theta+32138\right)-2^{24} x^{8}\left(602\theta^4+10928\theta^3+42765\theta^2+60182\theta+29287\right)+2^{26} x^{9}\left(2352\theta^4+7392\theta^3-7024\theta^2-31968\theta-21891\right)+2^{29} x^{10}\left(1584\theta^4+11904\theta^3+24696\theta^2+19776\theta+4915\right)-2^{35} x^{11}\left(16\theta^4-176\theta^3-784\theta^2-1036\theta-449\right)-2^{39} x^{12}\left((2\theta+3)^4\right)$

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Coefficients of the holomorphic solution: 1, -8, 112, -1152, 19216, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 7/2, 52, 500, 2796, ... ; Common denominator:...

#### Discriminant

$-(8z+1)(256z^2+16z-1)(1024z^3-160z^2-28z-1)^2(16z+1)^3$

#### Local exponents

$-\frac{ 1}{ 8}$$-\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}$$-\frac{ 1}{ 16}$ ≈$-0.057187-0.018391I$ ≈$-0.057187+0.018391I$$0$$-\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}$ ≈$0.270624$$\infty$
$0$$0$$0$$0$$0$$0$$0$$0$$\frac{ 3}{ 2}$
$1$$1$$0$$1$$1$$0$$1$$1$$\frac{ 3}{ 2}$
$1$$1$$0$$3$$3$$0$$1$$3$$\frac{ 3}{ 2}$
$2$$2$$0$$4$$4$$0$$2$$4$$\frac{ 3}{ 2}$

#### Note:

This is operator "12.17" from ...

4

New Number: 13.3 |  AESZ:  |  Superseeker: 4 52  |  Hash: 9127ce057848ca38f220a7bb67e245a2

Degree: 13

$\theta^4-2^{2} x\left(38\theta^4+50\theta^3+53\theta^2+28\theta+6\right)+2^{4} x^{2}\left(617\theta^4+1598\theta^3+2361\theta^2+1812\theta+586\right)-2^{8} x^{3}\left(1422\theta^4+5468\theta^3+10321\theta^2+9918\theta+3961\right)+2^{11} x^{4}\left(4165\theta^4+21060\theta^3+48228\theta^2+54855\theta+25440\right)-2^{14} x^{5}\left(8248\theta^4+50660\theta^3+135119\theta^2+175776\theta+91644\right)+2^{16} x^{6}\left(23161\theta^4+161282\theta^3+479205\theta^2+690060\theta+393943\right)-2^{20} x^{7}\left(12116\theta^4+89614\theta^3+279997\theta^2+425868\theta+256804\right)+2^{23} x^{8}\left(9924\theta^4+74644\theta^3+231233\theta^2+346097\theta+206261\right)-2^{27} x^{9}\left(3250\theta^4+24820\theta^3+75837\theta^2+107033\theta+58293\right)+2^{28} x^{10}\left(6672\theta^4+52000\theta^3+164304\theta^2+235440\theta+126113\right)-2^{32} x^{11}\left(1312\theta^4+10208\theta^3+32688\theta^2+49072\theta+28407\right)+2^{36} x^{12}\left(192\theta^4+1568\theta^3+4952\theta^2+7144\theta+3959\right)-2^{40} x^{13}\left((2\theta+5)^4\right)$

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Coefficients of the holomorphic solution: 1, 24, 464, 8832, 178960, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 7/2, 52, 500, 2796, ... ; Common denominator:...

#### Discriminant

$-(1-48z+256z^2)(8z-1)^2(512z^3-32z^2+20z-1)^2(16z-1)^3$

#### Local exponents

$0$ ≈$0.005863-0.196043I$ ≈$0.005863+0.196043I$$\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}$ ≈$0.050774$$\frac{ 1}{ 16}$$\frac{ 1}{ 8}$$\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$0$$\frac{ 5}{ 2}$
$0$$1$$1$$1$$1$$0$$0$$1$$\frac{ 5}{ 2}$
$0$$3$$3$$1$$3$$0$$-1$$1$$\frac{ 5}{ 2}$
$0$$4$$4$$2$$4$$0$$1$$2$$\frac{ 5}{ 2}$

#### Note:

This is operator "13.3" from ...

5

New Number: 8.69 |  AESZ:  |  Superseeker: 4 52  |  Hash: e303d10e77a367612be2fb706f37b895

Degree: 8

$\theta^4-2^{2} x\left(20\theta^4+34\theta^3+29\theta^2+12\theta+2\right)+2^{4} x^{2}\left(125\theta^4+362\theta^3+471\theta^2+284\theta+66\right)-2^{7} x^{3}\left(191\theta^4+606\theta^3+855\theta^2+588\theta+154\right)+2^{10} x^{4}\left(192\theta^4+552\theta^3+562\theta^2+268\theta+49\right)-2^{13} x^{5}\left(134\theta^4+380\theta^3+373\theta^2+124\theta+3\right)+2^{16} x^{6}\left(61\theta^4+150\theta^3+173\theta^2+93\theta+19\right)-2^{19} x^{7}\left(19\theta^4+50\theta^3+56\theta^2+31\theta+7\right)+2^{23} x^{8}\left((\theta+1)^4\right)$

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Coefficients of the holomorphic solution: 1, 8, 128, 2816, 74896, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 15/2, 52, 1563/2, 7276, ... ; Common denominator:...

#### Discriminant

$(16z-1)(8z-1)(64z^2-48z+1)(1-4z+32z^2)^2$

#### Local exponents

$0$$\frac{ 3}{ 8}-\frac{ 1}{ 4}\sqrt{ 2}$$\frac{ 1}{ 16}-\frac{ 1}{ 16}\sqrt{ 7}I$$\frac{ 1}{ 16}$$\frac{ 1}{ 16}+\frac{ 1}{ 16}\sqrt{ 7}I$$\frac{ 1}{ 8}$$\frac{ 3}{ 8}+\frac{ 1}{ 4}\sqrt{ 2}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$0$$1$$1$$1$$1$$1$$1$$1$
$0$$1$$3$$1$$3$$1$$1$$1$
$0$$2$$4$$2$$4$$2$$2$$1$

#### Note:

This is operator "8.69" from ...

6

New Number: 8.78 |  AESZ:  |  Superseeker: 52 48732  |  Hash: 2fb524ad6efb19e0117ae7acbd9f67b9

Degree: 8

$\theta^4-2^{2} x\left(184\theta^4+224\theta^3+175\theta^2+63\theta+9\right)+2^{4} 3 x^{2}\left(3472\theta^4+9664\theta^3+9864\theta^2+4264\theta+705\right)-2^{8} 3^{2} x^{3}\left(1936\theta^4+27936\theta^3+43336\theta^2+21528\theta+3933\right)-2^{16} 3^{3} x^{4}\left(1384\theta^4+524\theta^3-4555\theta^2-3404\theta-753\right)+2^{19} 3^{4} x^{5}\left(3440\theta^4+13712\theta^3-58\theta^2-3774\theta-1161\right)+2^{22} 3^{5} x^{6}\left(11312\theta^4-9888\theta^3-10808\theta^2-1608\theta+459\right)-2^{26} 3^{7} x^{7}(2\theta+1)(1336\theta^3+2772\theta^2+2234\theta+663)-2^{32} 3^{9} x^{8}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)$

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Coefficients of the holomorphic solution: 1, 36, 3780, 555120, 95199300, ...
--> OEIS
Normalized instanton numbers (n0=1): 52, -399, 48732, -992750, 98106208, ... ; Common denominator:...

#### Discriminant

$-(256z-1)(110592z^3+6912z^2-288z+1)(-1+96z+13824z^2)^2$

#### Local exponents

≈$-0.091906$$-\frac{ 1}{ 288}-\frac{ 1}{ 288}\sqrt{ 7}$$0$ ≈$0.00385$$\frac{ 1}{ 256}$$-\frac{ 1}{ 288}+\frac{ 1}{ 288}\sqrt{ 7}$ ≈$0.025556$$\infty$
$0$$0$$0$$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$1$$0$$1$$1$$1$$1$$\frac{ 3}{ 4}$
$1$$3$$0$$1$$1$$3$$1$$\frac{ 5}{ 4}$
$2$$4$$0$$2$$2$$4$$2$$\frac{ 3}{ 2}$

#### Note:

This is operator "8.78" from ...