### Summary

You searched for: sol=24

1

New Number: 2.14 |  AESZ: 48  |  Superseeker: 24 5832  |  Hash: 8081a3989d09a7d612953dac3341d90c

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 1800, 188160, 23423400, ...
--> OEIS
Normalized instanton numbers (n0=1): 24, 291/2, 5832, 247116, 12634944, ... ; Common denominator:...

#### Discriminant

$(216z-1)(108z-1)$

#### Local exponents

$0$$\frac{ 1}{ 216}$$\frac{ 1}{ 108}$$\infty$
$0$$0$$0$$\frac{ 1}{ 3}$
$0$$1$$1$$\frac{ 2}{ 3}$
$0$$1$$1$$\frac{ 4}{ 3}$
$0$$2$$2$$\frac{ 5}{ 3}$

#### Note:

B*d

2

New Number: 2.24 |  AESZ: 137  |  Superseeker: 20 1684/3  |  Hash: 198d6c822d6c46225ac2553d60df6539

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 1512, 124800, 11730600, ...
--> OEIS
Normalized instanton numbers (n0=1): 20, 2, 1684/3, 7602, 173472, ... ; Common denominator:...

#### Discriminant

$(144z-1)(128z-1)$

#### Local exponents

$0$$\frac{ 1}{ 144}$$\frac{ 1}{ 128}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$0$$1$$1$$\frac{ 1}{ 2}$
$0$$1$$1$$\frac{ 3}{ 2}$
$0$$2$$2$$\frac{ 3}{ 2}$

#### Note:

Hadamard product $A \ast g$.

3

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

Degree: 2

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

Maple   LaTex

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

4

New Number: 2.63 |  AESZ: 84  |  Superseeker: -4 -44  |  Hash: 908b978c0c447d3643c3018c40e7f5d1

Degree: 2

$\theta^4-2^{2} x\left(32\theta^4+64\theta^3+63\theta^2+31\theta+6\right)+2^{8} x^{2}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 936, 43008, 2145960, ...
--> OEIS
Normalized instanton numbers (n0=1): -4, -11, -44, -156, -288, ... ; Common denominator:...

#### Discriminant

$(64z-1)^2$

#### Local exponents

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

#### Note:

This is operator "2.63" from ...

5

New Number: 4.44 |  AESZ: 232  |  Superseeker: 379/5 1364199/5  |  Hash: 8d5ff690c87757ed51a092dee764eede

Degree: 4

$5^{2} \theta^4-5 x\left(2617\theta^4+4658\theta^3+3379\theta^2+1050\theta+120\right)+2^{6} 3 x^{2}\left(673\theta^4-4871\theta^3-10282\theta^2-5410\theta-860\right)+2^{10} 3^{2} x^{3}\left(955\theta^4+4320\theta^3+3477\theta^2+1020\theta+100\right)-2^{17} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 3960, 974400, 292030200, ...
--> OEIS
Normalized instanton numbers (n0=1): 379/5, 3346, 1364199/5, 177727432/5, 5658116533, ... ; Common denominator:...

#### Discriminant

$-(27z+1)(512z-1)(-5+96z)^2$

#### Local exponents

$-\frac{ 1}{ 27}$$0$$\frac{ 1}{ 512}$$\frac{ 5}{ 96}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 3}$
$1$$0$$1$$1$$\frac{ 1}{ 2}$
$1$$0$$1$$3$$\frac{ 1}{ 2}$
$2$$0$$2$$4$$\frac{ 2}{ 3}$

#### Note:

6

New Number: 4.69 |  AESZ: 350  |  Superseeker: 49 173876/9  |  Hash: e6de16eb3758d2ed5687f4b2a2abf36b

Degree: 4

$\theta^4-x\left(24+184\theta+545\theta^2+722\theta^3+289\theta^4\right)+2^{3} 3 x^{2}\left(214\theta^4+2734\theta^3+4861\theta^2+2640\theta+468\right)+2^{6} 3^{2} x^{3}\left(1391\theta^4+5184\theta^3+4252\theta^2+1296\theta+126\right)+2^{10} 3^{6} x^{4}\left((2\theta+1)^4\right)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 1944, 232800, 34133400, ...
--> OEIS
Normalized instanton numbers (n0=1): 49, 136, 173876/9, 781152, 57087750, ... ; Common denominator:...

#### Discriminant

$(256z-1)(81z-1)(1+24z)^2$

#### Local exponents

$-\frac{ 1}{ 24}$$0$$\frac{ 1}{ 256}$$\frac{ 1}{ 81}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$0$$1$$1$$\frac{ 1}{ 2}$
$3$$0$$1$$1$$\frac{ 1}{ 2}$
$4$$0$$2$$2$$\frac{ 1}{ 2}$

#### Note:

Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ 351/4.70

7

New Number: 5.100 |  AESZ: 347  |  Superseeker: 15 27140/3  |  Hash: f00de20026c099e75b447c475ab287e4

Degree: 5

$\theta^4-3 x\left(213\theta^4+186\theta^3+149\theta^2+56\theta+8\right)+2^{3} 3^{3} x^{2}\left(702\theta^4+1078\theta^3+949\theta^2+392\theta+60\right)-2^{6} 3^{3} x^{3}\left(9277\theta^4+18432\theta^3+16008\theta^2+6000\theta+840\right)+2^{13} 3^{4} 5 x^{4}(2\theta+1)^2(51\theta^2+69\theta+32)-2^{14} 3^{6} 5^{2} x^{5}(2\theta+1)^2(2\theta+3)^2$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 1944, 218400, 28488600, ...
--> OEIS
Normalized instanton numbers (n0=1): 15, 1329/4, 27140/3, 220680, 5952570, ... ; Common denominator:...

#### Discriminant

$-(192z-1)(1728z^2-207z+1)(-1+120z)^2$

#### Local exponents

$0$$\frac{ 23}{ 384}-\frac{ 11}{ 1152}\sqrt{ 33}$$\frac{ 1}{ 192}$$\frac{ 1}{ 120}$$\frac{ 23}{ 384}+\frac{ 11}{ 1152}\sqrt{ 33}$$\infty$
$0$$0$$0$$0$$0$$\frac{ 1}{ 2}$
$0$$1$$1$$1$$1$$\frac{ 1}{ 2}$
$0$$1$$1$$3$$1$$\frac{ 3}{ 2}$
$0$$2$$2$$4$$2$$\frac{ 3}{ 2}$

#### Note:

This is operator "5.100" from ...

8

New Number: 5.12 |  AESZ: 74  |  Superseeker: -30 -14632  |  Hash: e668180adb7c88d4e5fbab5eb7ee61c7

Degree: 5

$\theta^4-2 3 x\left(99\theta^4+36\theta^3+39\theta^2+21\theta+4\right)+2^{2} 3^{2} x^{2}\left(3807\theta^4+3564\theta^3+3798\theta^2+1683\theta+284\right)-2^{3} 3^{5} x^{3}\left(7857\theta^4+13608\theta^3+14562\theta^2+7317\theta+1444\right)+2^{4} 3^{9} x^{4}\left(2592\theta^4+7128\theta^3+8550\theta^2+4851\theta+1052\right)-2^{5} 3^{13} x^{5}(3\theta+2)(3\theta+4)(6\theta+5)(6\theta+7)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 1152, 71520, 5101200, ...
--> OEIS
Normalized instanton numbers (n0=1): -30, -516, -14632, -4227807/8, -22139868, ... ; Common denominator:...

#### Discriminant

$-(-1+54z)(162z-1)^2(108z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 162}$$\frac{ 1}{ 108}$$\frac{ 1}{ 54}$$\infty$
$0$$0$$0$$0$$\frac{ 2}{ 3}$
$0$$1$$\frac{ 1}{ 2}$$1$$\frac{ 5}{ 6}$
$0$$3$$\frac{ 1}{ 2}$$1$$\frac{ 7}{ 6}$
$0$$4$$1$$2$$\frac{ 4}{ 3}$

#### Note:

This is operator "5.12" from ...

9

New Number: 5.17 |  AESZ: 119  |  Superseeker: 28/3 3892/3  |  Hash: dc8ec37012f2c92c83e6519935956eeb

Degree: 5

$3^{2} \theta^4-2^{2} 3 x\left(256\theta^4+320\theta^3+271\theta^2+111\theta+18\right)+2^{7} x^{2}\left(3104\theta^4+7040\theta^3+8012\theta^2+4452\theta+927\right)-2^{15} x^{3}\left(752\theta^4+2304\theta^3+3042\theta^2+1854\theta+405\right)+2^{21} x^{4}(2\theta+1)(176\theta^3+552\theta^2+622\theta+231)-2^{31} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 1128, 67200, 4634280, ...
--> OEIS
Normalized instanton numbers (n0=1): 28/3, 394/3, 3892/3, 108262/3, 1044128, ... ; Common denominator:...

#### Discriminant

$-(-1+128z)(64z-1)^2(128z-3)^2$

#### Local exponents

$0$$\frac{ 1}{ 128}$$\frac{ 1}{ 64}$$\frac{ 3}{ 128}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 2}$
$0$$1$$\frac{ 1}{ 4}$$1$$1$
$0$$1$$\frac{ 3}{ 4}$$3$$1$
$0$$2$$1$$4$$\frac{ 3}{ 2}$

#### Note:

This is operator "5.17" from ...

10

New Number: 5.32 |  AESZ: 215  |  Superseeker: 220/3 89212  |  Hash: ced61f5675491a3c4446c0e55e7bc36b

Degree: 5

$3^{2} \theta^4-2^{2} 3 x\left(268\theta^4+632\theta^3+463\theta^2+147\theta+18\right)-2^{7} x^{2}\left(448\theta^4-1616\theta^3-4280\theta^2-2418\theta-441\right)+2^{12} x^{3}\left(416\theta^4+2016\theta^3+756\theta^2-288\theta-135\right)+2^{19} x^{4}(8\theta^2-28\theta-33)(2\theta+1)^2-2^{24} x^{5}(2\theta+1)^2(2\theta+3)^2$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 2664, 470400, 102047400, ...
--> OEIS
Normalized instanton numbers (n0=1): 220/3, 3538/3, 89212, 7484350, 2459418080/3, ... ; Common denominator:...

#### Discriminant

$-(16z-1)(4096z^2-384z+1)(3+64z)^2$

#### Local exponents

$-\frac{ 3}{ 64}$$0$$\frac{ 3}{ 64}-\frac{ 1}{ 32}\sqrt{ 2}$$\frac{ 1}{ 16}$$\frac{ 3}{ 64}+\frac{ 1}{ 32}\sqrt{ 2}$$\infty$
$0$$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$0$$1$$1$$1$$\frac{ 1}{ 2}$
$3$$0$$1$$1$$1$$\frac{ 3}{ 2}$
$4$$0$$2$$2$$2$$\frac{ 3}{ 2}$

#### Note:

This is operator "5.32" from ...

11

New Number: 5.83 |  AESZ: 316  |  Superseeker: 852/11 1678156/11  |  Hash: b8201d587a016cc013e2477aadb5c1ff

Degree: 5

$11^{2} \theta^4-2^{2} 3 11 x\left(364\theta^4+824\theta^3+599\theta^2+187\theta+22\right)-2^{5} x^{2}\left(62164\theta^4+84496\theta^3+12499\theta^2-6402\theta-1584\right)-2^{4} 3 x^{3}\left(484016\theta^4+474144\theta^3+366952\theta^2+161832\theta+27027\right)-2^{11} 3^{2} x^{4}(964\theta^2+1360\theta+669)(2\theta+1)^2-2^{16} 3^{4} x^{5}(2\theta+1)^2(2\theta+3)^2$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 3240, 675600, 171901800, ...
--> OEIS
Normalized instanton numbers (n0=1): 852/11, 21572/11, 1678156/11, 15912512, 22956446184/11, ... ; Common denominator:...

#### Discriminant

$-(2304z^3+1664z^2+432z-1)(11+192z)^2$

#### Local exponents

≈$-0.362258-0.240689I$ ≈$-0.362258+0.240689I$$-\frac{ 11}{ 192}$$0$ ≈$0.002294$$\infty$
$0$$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$1$$1$$0$$1$$\frac{ 1}{ 2}$
$1$$1$$3$$0$$1$$\frac{ 3}{ 2}$
$2$$2$$4$$0$$2$$\frac{ 3}{ 2}$

#### Note:

This is operator "5.83" from ...

12

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

Degree: 13

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

Maple   LaTex

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 ...

13

New Number: 6.14 |  AESZ:  |  Superseeker: 8 9928/3  |  Hash: 44968de144621e2fa74ce3964a5435f7

Degree: 6

$\theta^4-2^{2} x(5\theta^2+5\theta+2)(13\theta^2+13\theta+3)+2^{5} x^{2}\left(533\theta^4+2132\theta^3+3137\theta^2+2010\theta+432\right)-2^{8} 3 x^{3}\left(652\theta^4+3912\theta^3+8229\theta^2+7083\theta+1845\right)+2^{12} 3^{2} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)-2^{15} 3^{3} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2+2^{17} 3^{4} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 1224, 96000, 9633960, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, 471/2, 9928/3, 185385, 6071232, ... ; Common denominator:...

#### Discriminant

$(12z-1)(24z-1)(2304z^2-192z+1)(-1+16z)^2$

#### Local exponents

$0$$\frac{ 1}{ 24}-\frac{ 1}{ 48}\sqrt{ 3}$$\frac{ 1}{ 24}$$\frac{ 1}{ 16}$$\frac{ 1}{ 24}+\frac{ 1}{ 48}\sqrt{ 3}$$\frac{ 1}{ 12}$$\infty$
$0$$0$$0$$0$$0$$0$$\frac{ 1}{ 2}$
$0$$1$$1$$\frac{ 1}{ 2}$$1$$1$$\frac{ 5}{ 2}$
$0$$1$$1$$\frac{ 1}{ 2}$$1$$1$$\frac{ 7}{ 2}$
$0$$2$$2$$1$$2$$2$$\frac{ 11}{ 2}$

#### Note:

This is operator "6.14" from ...

14

New Number: 7.3 |  AESZ:  |  Superseeker: 3 64  |  Hash: 8413250555ca536f1bdccfeed506ea4e

Degree: 7

$\theta^4+x\theta(39\theta^3-30\theta^2-19\theta-4)+2 x^{2}\left(16\theta^4-1070\theta^3-1057\theta^2-676\theta-192\right)-2^{2} 3^{2} x^{3}(3\theta+2)(171\theta^3+566\theta^2+600\theta+316)-2^{5} 3^{3} x^{4}\left(384\theta^4+1542\theta^3+2635\theta^2+2173\theta+702\right)-2^{6} 3^{3} x^{5}(\theta+1)(1393\theta^3+5571\theta^2+8378\theta+4584)-2^{10} 3^{5} x^{6}(\theta+1)(\theta+2)(31\theta^2+105\theta+98)-2^{12} 3^{7} x^{7}(\theta+1)(\theta+2)^2(\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 24, 192, 3384, ...
--> OEIS
Normalized instanton numbers (n0=1): 3, -4, 64, -253, 4292, ... ; Common denominator:...

#### Discriminant

$-(8z+1)(24z-1)(3z+1)(4z+1)(12z+1)(1+18z)^2$

#### Local exponents

$-\frac{ 1}{ 3}$$-\frac{ 1}{ 4}$$-\frac{ 1}{ 8}$$-\frac{ 1}{ 12}$$-\frac{ 1}{ 18}$$0$$\frac{ 1}{ 24}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$1$$1$$1$$0$$1$$2$
$1$$1$$1$$1$$3$$0$$1$$2$
$2$$2$$2$$2$$4$$0$$2$$3$

#### Note:

This is operator "7.3" from ...

15

New Number: 8.14 |  AESZ: 176  |  Superseeker: 24 15448/3  |  Hash: e2a40a57f7e88dba6655d936b4abe327

Degree: 8

$\theta^4-2^{2} x(3\theta^2+3\theta+1)(17\theta^2+17\theta+6)+2^{5} x^{2}\left(325\theta^4+2164\theta^3+3053\theta^2+1778\theta+420\right)+2^{10} 3^{2} x^{3}\left(51\theta^4-306\theta^3-934\theta^2-717\theta-204\right)-2^{14} 3^{2} x^{4}\left(397\theta^4+794\theta^3-1454\theta^2-1851\theta-666\right)+2^{18} 3^{4} x^{5}\left(51\theta^4+510\theta^3+290\theta^2-29\theta-64\right)+2^{21} 3^{4} x^{6}\left(325\theta^4-864\theta^3-1489\theta^2-864\theta-144\right)-2^{26} 3^{6} x^{7}(3\theta^2+3\theta+1)(17\theta^2+17\theta+6)+2^{32} 3^{8} x^{8}\left((\theta+1)^4\right)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 840, 34944, 1618344, ...
--> OEIS
Normalized instanton numbers (n0=1): 24, -509/2, 15448/3, -128530, 3746624, ... ; Common denominator:...

#### Discriminant

$(72z-1)(36z-1)(64z-1)(32z-1)(48z-1)^2(48z+1)^2$

#### Local exponents

$-\frac{ 1}{ 48}$$0$$\frac{ 1}{ 72}$$\frac{ 1}{ 64}$$\frac{ 1}{ 48}$$\frac{ 1}{ 36}$$\frac{ 1}{ 32}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$1$$0$$1$$1$$1$$1$$1$$1$
$3$$0$$1$$1$$3$$1$$1$$1$
$4$$0$$2$$2$$4$$2$$2$$1$

#### Note:

Hadamard product $d \ast g$. This operator has a second MUM-point at infinity with the same instanton numbers. It
can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\sqrt{?})$.

16

New Number: 8.54 |  AESZ:  |  Superseeker: 0 1/3  |  Hash: bb80872017d0578a4ae56172666b807c

Degree: 8

$\theta^4+x\theta(3\theta^3-6\theta^2-4\theta-1)-x^{2}\left(211\theta^4+856\theta^3+1433\theta^2+1184\theta+384\right)-2 x^{3}\left(761\theta^4+3288\theta^3+6477\theta^2+6654\theta+2700\right)+2^{2} x^{4}(\theta+1)(2013\theta^3+17379\theta^2+40726\theta+28548)+2^{3} x^{5}(\theta+1)(15719\theta^3+126105\theta^2+325408\theta+269508)+2^{5} 3^{2} x^{6}(\theta+1)(\theta+2)(1817\theta^2+11967\theta+19631)+2^{7} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(89\theta+350)+2^{9} 3^{3} 43 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 24, 72, 1296, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, 1/2, 1/3, -1, 2, ... ; Common denominator:...

#### Discriminant

$(4z+1)(6z+1)(43z^2+13z+1)(2z+1)^2(12z-1)^2$

#### Local exponents

$-\frac{ 1}{ 2}$$-\frac{ 1}{ 4}$$-\frac{ 1}{ 6}$$-\frac{ 13}{ 86}-\frac{ 1}{ 86}\sqrt{ 3}I$$-\frac{ 13}{ 86}+\frac{ 1}{ 86}\sqrt{ 3}I$$0$$\frac{ 1}{ 12}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$1$$1$$1$$0$$\frac{ 1}{ 2}$$2$
$3$$1$$1$$1$$1$$0$$\frac{ 1}{ 2}$$3$
$4$$2$$2$$2$$2$$0$$1$$4$

#### Note:

This is operator "8.54" from ...

17

New Number: 8.68 |  AESZ:  |  Superseeker: 6/17 33/17  |  Hash: 0c0662f5b46ac6cb0bd298a63cf364c7

Degree: 8

$17^{2} \theta^4+17 x\theta(165\theta^3-114\theta^2-74\theta-17)-x^{2}\left(20619\theta^4+122880\theta^3+175353\theta^2+126480\theta+36992\right)-2 x^{3}\left(201857\theta^4+853944\theta^3+1437673\theta^2+1174122\theta+375972\right)-2^{2} x^{4}\left(571275\theta^4+2711616\theta^3+5301571\theta^2+4856674\theta+1694372\right)-2^{3} 3 x^{5}(\theta+1)(295815\theta^3+1523993\theta^2+2924668\theta+1983212)-2^{5} x^{6}(\theta+1)(\theta+2)(558823\theta^2+2951265\theta+4136951)-2^{7} 3 37 x^{7}(\theta+3)(\theta+2)(\theta+1)(2797\theta+9878)-2^{9} 3^{2} 7 37^{2} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 8, 24, 288, ...
--> OEIS
Normalized instanton numbers (n0=1): 6/17, 25/34, 33/17, 157/17, 577/17, ... ; Common denominator:...

#### Discriminant

$-(12z-1)(6z+1)(7z^2-z+1)(4z+1)^2(74z+17)^2$

#### Local exponents

$-\frac{ 1}{ 4}$$-\frac{ 17}{ 74}$$-\frac{ 1}{ 6}$$0$$\frac{ 1}{ 14}-\frac{ 3}{ 14}\sqrt{ 3}I$$\frac{ 1}{ 14}+\frac{ 3}{ 14}\sqrt{ 3}I$$\frac{ 1}{ 12}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$\frac{ 1}{ 2}$$1$$1$$0$$1$$1$$1$$2$
$\frac{ 1}{ 2}$$3$$1$$0$$1$$1$$1$$3$
$1$$4$$2$$0$$2$$2$$2$$4$

#### Note:

This is operator "8.68" from ...

18

New Number: 8.82 |  AESZ:  |  Superseeker: 0 -1/3  |  Hash: 8bab1ddc8b31cb2c21f01402f27895ce

Degree: 8

$\theta^4-x\theta(3\theta^3-6\theta^2-4\theta-1)-x^{2}\left(211\theta^4+856\theta^3+1433\theta^2+1184\theta+384\right)+2 x^{3}\left(761\theta^4+3288\theta^3+6477\theta^2+6654\theta+2700\right)+2^{2} x^{4}(\theta+1)(2013\theta^3+17379\theta^2+40726\theta+28548)-2^{3} x^{5}(\theta+1)(15719\theta^3+126105\theta^2+325408\theta+269508)+2^{5} 3^{2} x^{6}(\theta+1)(\theta+2)(1817\theta^2+11967\theta+19631)-2^{7} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(89\theta+350)+2^{9} 3^{3} 43 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 24, -72, 1296, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, 1/2, -1/3, -1, -2, ... ; Common denominator:...

#### Discriminant

$(6z-1)(4z-1)(43z^2-13z+1)(12z+1)^2(-1+2z)^2$

#### Local exponents

$-\frac{ 1}{ 12}$$0$$\frac{ 13}{ 86}-\frac{ 1}{ 86}\sqrt{ 3}I$$\frac{ 13}{ 86}+\frac{ 1}{ 86}\sqrt{ 3}I$$\frac{ 1}{ 6}$$\frac{ 1}{ 4}$$\frac{ 1}{ 2}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$\frac{ 1}{ 2}$$0$$1$$1$$1$$1$$1$$2$
$\frac{ 1}{ 2}$$0$$1$$1$$1$$1$$3$$3$
$1$$0$$2$$2$$2$$2$$4$$4$

#### Note:

This is operator "8.82" from ...

19

New Number: 8.85 |  AESZ:  |  Superseeker: 196 1986884/3  |  Hash: d959f61fe3ba327116d3bae5ae5a0ade

Degree: 8

$\theta^4+2^{2} x\left(68\theta^4-296\theta^3-201\theta^2-53\theta-6\right)-2^{7} x^{2}\left(1192\theta^4+2392\theta^3-1108\theta^2-439\theta-57\right)-2^{12} 3^{2} x^{3}\left(881\theta^4-450\theta^3+2012\theta^2+915\theta+153\right)+2^{16} 3^{2} x^{4}\left(7060\theta^4-11260\theta^3-6320\theta^2-3471\theta-783\right)+2^{20} 3^{4} x^{5}\left(308\theta^4+5480\theta^3-2459\theta^2-3341\theta-990\right)-2^{26} 3^{4} x^{6}\left(2174\theta^4+2754\theta^3+3787\theta^2+2808\theta+801\right)+2^{30} 3^{6} 5 x^{7}(107\theta^2+216\theta+108)(\theta+1)^2-2^{36} 3^{8} 5^{2} x^{8}\left((\theta+1)^4\right)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 2472, 412800, 83283624, ...
--> OEIS
Normalized instanton numbers (n0=1): 196, -5988, 1986884/3, -62128884, 8854857504, ... ; Common denominator:...

#### Discriminant

$-(64z+1)(331776z^3-9216z^2+368z-1)(-1-288z+23040z^2)^2$

#### Local exponents

$-\frac{ 1}{ 64}$$\frac{ 1}{ 160}-\frac{ 1}{ 480}\sqrt{ 19}$$0$ ≈$0.002907$ ≈$0.012435-0.029703I$ ≈$0.012435+0.029703I$$\frac{ 1}{ 160}+\frac{ 1}{ 480}\sqrt{ 19}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$0$$1$$1$$1$$1$$1$
$1$$3$$0$$1$$1$$1$$3$$1$
$2$$4$$0$$2$$2$$2$$4$$1$

#### Note:

This is operator "8.85" from ...

20

New Number: 9.2 |  AESZ:  |  Superseeker: 9/7 49/3  |  Hash: 356d4564e48d7a04e815fa223b6ccc46

Degree: 9

$7^{2} \theta^4+7 x\theta(165\theta^3-102\theta^2-65\theta-14)-2^{3} x^{2}\left(920\theta^4+11726\theta^3+15277\theta^2+9478\theta+2352\right)-2^{4} 3^{2} x^{3}\left(4035\theta^4+19554\theta^3+29157\theta^2+20706\theta+5761\right)-2^{8} 3^{2} x^{4}\left(4156\theta^4+17951\theta^3+28198\theta^2+21045\theta+6096\right)-2^{11} 3^{3} x^{5}\left(1538\theta^4+6560\theta^3+10755\theta^2+8234\theta+2420\right)-2^{13} 3^{4} x^{6}\left(695\theta^4+3051\theta^3+5285\theta^2+4191\theta+1259\right)-2^{14} 3^{5} x^{7}\left(385\theta^4+1802\theta^3+3319\theta^2+2754\theta+855\right)-2^{18} 3^{6} x^{8}(\theta+1)^2(15\theta^2+48\theta+43)-2^{20} 3^{7} x^{9}(\theta+1)^2(\theta+2)^2$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 24, 144, 3240, ...
--> OEIS
Normalized instanton numbers (n0=1): 9/7, 47/7, 49/3, 1370/7, 10063/7, ... ; Common denominator:...

#### Discriminant

$-(8z+1)(24z-1)(3z+1)(4z+1)(12z+1)(7+72z+288z^2)^2$

#### Local exponents

$-\frac{ 1}{ 3}$$-\frac{ 1}{ 4}$$-\frac{ 1}{ 8}-\frac{ 1}{ 24}\sqrt{ 5}I$$-\frac{ 1}{ 8}$$-\frac{ 1}{ 8}+\frac{ 1}{ 24}\sqrt{ 5}I$$-\frac{ 1}{ 12}$$0$$\frac{ 1}{ 24}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$1$$1$$1$$1$$0$$1$$1$
$1$$1$$3$$1$$3$$1$$0$$1$$2$
$2$$2$$4$$2$$4$$2$$0$$2$$2$

#### Note:

This is operator "9.2" from ...

21

New Number: 1.5 |  AESZ: 5  |  Superseeker: 60 134292  |  Hash: a6c4fb927cb2a4bb1103c1c739a252b0

Degree: 1

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 3240, 672000, 169785000, ...
--> OEIS
Normalized instanton numbers (n0=1): 60, 1869, 134292, 14016600, 1806410976, ... ; Common denominator:...

#### Discriminant

$1-432z$

#### Local exponents

$0$$\frac{ 1}{ 432}$$\infty$
$0$$0$$\frac{ 1}{ 3}$
$0$$1$$\frac{ 1}{ 2}$
$0$$1$$\frac{ 1}{ 2}$
$0$$2$$\frac{ 2}{ 3}$

#### Note:

A-incarnation: X(2,2,3) in $P^6$.