### Summary

You searched for: inst=10

1

New Number: 2.61 |  AESZ: 26  |  Superseeker: 10 1724  |  Hash: f3fc09474973b19b8bdb783e3322eb65

Degree: 2

$\theta^4-2 x(2\theta+1)^2(13\theta^2+13\theta+4)-2^{2} 3 x^{2}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 288, 15200, 968800, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, 191/2, 1724, 45680, 1478214, ... ; Common denominator:...

#### Discriminant

$-(4z+1)(108z-1)$

#### Local exponents

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

#### Note:

A-incarnation: $X(1,1,1,1,2) \subset Grass(2,6)$

2

New Number: 3.10 |  AESZ: ~103  |  Superseeker: 10 664  |  Hash: 9239615e8ac132ca232c13367a39ae3b

Degree: 3

$\theta^4-2 x\left(86\theta^4+172\theta^3+143\theta^2+57\theta+9\right)+2^{2} 3^{2} x^{2}(\theta+1)^2(236\theta^2+472\theta+187)-2^{4} 3^{4} 5^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 630, 28980, 1593270, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, 24, 664, 9088, 234388, ... ; Common denominator:...

#### Discriminant

$-(100z-1)(-1+36z)^2$

#### Local exponents

$0$$\frac{ 1}{ 100}$$\frac{ 1}{ 36}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$0$$1$$\frac{ 1}{ 2}$$1$
$0$$1$$\frac{ 1}{ 2}$$2$
$0$$2$$1$$\frac{ 5}{ 2}$

#### Note:

Operator equivalent to AESZ 103 =$c \ast c$.

3

New Number: 3.16 |  AESZ: 386  |  Superseeker: 10 18328  |  Hash: 7d032616d3bd41272e22a4d23747d7a0

Degree: 3

$\theta^4-2 x\left(422\theta^4+844\theta^3+751\theta^2+329\theta+57\right)+2^{2} 3^{4} x^{2}(\theta+1)^2(716\theta^2+1432\theta+579)-2^{4} 3^{8} 7^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 114, 22518, 5236980, 1321024950, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, -872, 18328, -432528, 13706388, ... ; Common denominator:...

#### Discriminant

$-(196z-1)(-1+324z)^2$

#### Local exponents

$0$$\frac{ 1}{ 324}$$\frac{ 1}{ 196}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$0$$0$$1$$1$
$0$$1$$1$$2$
$0$$1$$2$$\frac{ 5}{ 2}$

4

New Number: 4.28 |  AESZ: 244  |  Superseeker: 10 1018  |  Hash: 6bf8549841e32615ff2b7798191c0de3

Degree: 4

$\theta^4+x\left(208\theta^4+416\theta^3+504\theta^2+296\theta+67\right)+x^{2}\left(9952\theta^4+39808\theta^3+57734\theta^2+35852\theta+7665\right)-2^{3} 3 x^{3}\left(3744\theta^4+22464\theta^3+53974\theta^2+60834\theta+26775\right)+3^{2} x^{4}(12\theta+23)^2(12\theta+25)^2$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -67, 11529/2, -1062425/2, 406816235/8, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, -167/2, 1018, -16457, 304664, ... ; Common denominator:...

#### Discriminant

$(108z+1)^2(4z-1)^2$

No data for singularities

#### Note:

5

New Number: 5.68 |  AESZ: 279  |  Superseeker: -10/17 10  |  Hash: 06f80606fbeb2b0cc9559df633f1f59d

Degree: 5

$17^{2} \theta^4+17 x\left(286\theta^4+734\theta^3+656\theta^2+289\theta+51\right)+3^{2} x^{2}\left(4110\theta^4+22074\theta^3+37209\theta^2+26265\theta+6800\right)-3^{5} x^{3}\left(1521\theta^4+7344\theta^3+12936\theta^2+9945\theta+2822\right)+3^{8} x^{4}\left(123\theta^4+552\theta^3+879\theta^2+603\theta+152\right)-3^{12} x^{5}\left((\theta+1)^4\right)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -3, 9, 51, -1431, ...
--> OEIS
Normalized instanton numbers (n0=1): -10/17, -19/17, 10, -369/17, -1413/17, ... ; Common denominator:...

#### Discriminant

$-(729z^3-189z^2-20z-1)(-17+27z)^2$

#### Local exponents

≈$-0.044921-0.04372I$ ≈$-0.044921+0.04372I$$0$ ≈$0.349102$$\frac{ 17}{ 27}$$\infty$
$0$$0$$0$$0$$0$$1$
$1$$1$$0$$1$$1$$1$
$1$$1$$0$$1$$3$$1$
$2$$2$$0$$2$$4$$1$

#### Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 280/5.69

6

New Number: 10.4 |  AESZ:  |  Superseeker: 10 7709/9  |  Hash: 6162ae56594cb4ca6830174a8ed00300

Degree: 10

$\theta^4+x\left(14+63\theta+102\theta^2+78\theta^3+231\theta^4\right)+x^{2}\left(2832+13390\theta+24563\theta^2+19308\theta^3+21987\theta^4\right)+2^{3} x^{3}\left(140700\theta^4+225708\theta^3+290537\theta^2+177465\theta+44084\right)+2^{4} 3 x^{4}\left(713295\theta^4+1769710\theta^3+2523886\theta^2+1767335\theta+499986\right)+2^{6} x^{5}\left(10296675\theta^4+36211314\theta^3+60921650\theta^2+49433683\theta+15811528\right)+2^{6} x^{6}\left(137088291\theta^4+659829216\theta^3+1356977569\theta^2+1291863456\theta+467669756\right)+2^{9} x^{7}\left(179375706\theta^4+1143044916\theta^3+2845532295\theta^2+3114799053\theta+1242790862\right)+2^{12} x^{8}\left(184827267\theta^4+1416425484\theta^3+3980381306\theta^2+4736268700\theta+1991273435\right)+2^{16} 47 x^{9}(2\theta+3)(622034\theta^3+4130865\theta^2+8390461\theta+4891218)+2^{20} 3 17^{2} 47^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -14, 250, -5192, 116266, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, -149/2, 7709/9, -27333/2, 242829, ... ; Common denominator:...

#### Discriminant

$(24z+1)(2312z^3+75z^2+15z+1)(32z+1)^2(376z^2+64z+1)^2$

#### Local exponents

$-\frac{ 4}{ 47}-\frac{ 9}{ 188}\sqrt{ 2}$ ≈$-0.055617$$-\frac{ 1}{ 24}$$-\frac{ 1}{ 32}$$-\frac{ 4}{ 47}+\frac{ 9}{ 188}\sqrt{ 2}$$0$ ≈$0.011589-0.087422I$ ≈$0.011589+0.087422I$$\infty$
$0$$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$1$$\frac{ 1}{ 2}$$1$$0$$1$$1$$\frac{ 3}{ 2}$
$3$$1$$1$$\frac{ 1}{ 2}$$3$$0$$1$$1$$\frac{ 5}{ 2}$
$4$$2$$2$$1$$4$$0$$2$$2$$3$

#### Note:

This is operator "10.4" from ...

7

New Number: 11.14 |  AESZ:  |  Superseeker: 10 13958/9  |  Hash: 0a4e6572e1bb29d996fd62dc404c2446

Degree: 11

$3^{6} \theta^4-3^{6} x\left(111\theta^4+180\theta^3+140\theta^2+50\theta+7\right)+3^{3} x^{2}\left(31925\theta^4+11480\theta^3-42466\theta^2-34182\theta-7560\right)+3^{3} x^{3}\left(4877\theta^4+370644\theta^3+409430\theta^2+199476\theta+42297\right)-2 x^{4}\left(10348339\theta^4+26540048\theta^3+42009388\theta^2+29955528\theta+7880058\right)+2 x^{5}\left(9831565\theta^4+67438924\theta^3+143690304\theta^2+116711926\theta+33599143\right)+2 x^{6}\left(14540887\theta^4-5897448\theta^3-129216202\theta^2-158647410\theta-56400514\right)-2 x^{7}\left(20947985\theta^4+93882580\theta^3+71337738\theta^2-9343940\theta-17269525\right)+x^{8}\left(1325117\theta^4+114002144\theta^3+209338120\theta^2+141064960\theta+32960772\right)+3^{4} x^{9}\left(254941\theta^4+471612\theta^3+445052\theta^2+300870\theta+101457\right)-3^{8} x^{10}\left(1621\theta^4+5816\theta^3+8326\theta^2+5418\theta+1332\right)+3^{13} x^{11}\left((\theta+1)^4\right)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 7, 231, 11185, 654199, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, 2591/27, 13958/9, 1037839/27, 3535478/3, ... ; Common denominator:...

#### Discriminant

$(z-1)(243z^4-520z^3+310z^2+96z-1)(27-189z-143z^2+81z^3)^2$

#### Local exponents

≈$-0.97581$$0$ ≈$0.130861$$1$ ≈$2.610381$$#ND+#NDI$$\infty$
$0$$0$$0$$0$$0$$0$$1$
$1$$0$$1$$1$$1$$1$$1$
$3$$0$$3$$1$$3$$1$$1$
$4$$0$$4$$2$$4$$2$$1$

#### Note:

This is operator "11.14" from ...

8

New Number: 13.7 |  AESZ:  |  Superseeker: 10 7709/9  |  Hash: 47093f7f3b7ab4544ef6b418bdae778b

Degree: 13

$\theta^4+x\left(127\theta^4-2\theta^3+22\theta^2+23\theta+6\right)+x^{2}\left(4803\theta^4+1644\theta^3+3459\theta^2+430\theta-384\right)+2^{3} x^{3}\left(2507\theta^4+8118\theta^3-2448\theta^2-7127\theta-2940\right)-2^{4} x^{4}\left(94175\theta^4+88358\theta^3+133418\theta^2+111507\theta+38898\right)+2^{6} 3 x^{5}\left(22347\theta^4+197706\theta^3+783766\theta^2+893091\theta+359952\right)+2^{6} 3^{2} x^{6}\left(869067\theta^4+4718208\theta^3+11162457\theta^2+11758320\theta+4583500\right)-2^{9} 3^{3} x^{7}\left(245985\theta^4+1338174\theta^3+3414812\theta^2+4418167\theta+2103502\right)-2^{12} 3^{4} x^{8}\left(234234\theta^4+2167368\theta^3+7012373\theta^2+9416514\theta+4375751\right)+2^{15} 3^{5} x^{9}\left(81234\theta^4+643380\theta^3+1815861\theta^2+2193249\theta+947968\right)+2^{18} 3^{6} x^{10}(\theta+1)(15879\theta^3+214401\theta^2+816191\theta+896789)-2^{21} 3^{7} x^{11}(\theta+1)(\theta+2)(8037\theta^2+71103\theta+151546)+2^{27} 3^{9} x^{12}(\theta+3)(\theta+2)(\theta+1)(31\theta+152)-2^{29} 3^{9} 5 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -6, 90, -1368, 21546, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, -149/2, 7709/9, -27333/2, 242829, ... ; Common denominator:...

#### Discriminant

$-(16z+1)(2160z^3+27z^2-9z+1)(24z+1)^2(72z^2-48z-1)^2(8z-1)^3$

#### Local exponents

≈$-0.100198$$-\frac{ 1}{ 16}$$-\frac{ 1}{ 24}$$\frac{ 1}{ 3}-\frac{ 1}{ 4}\sqrt{ 2}$$0$ ≈$0.043849-0.05194I$ ≈$0.043849+0.05194I$$\frac{ 1}{ 8}$$\frac{ 1}{ 3}+\frac{ 1}{ 4}\sqrt{ 2}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$\frac{ 1}{ 2}$$1$$0$$1$$1$$\frac{ 1}{ 2}$$1$$2$
$1$$1$$\frac{ 1}{ 2}$$3$$0$$1$$1$$\frac{ 3}{ 2}$$3$$3$
$2$$2$$1$$4$$0$$2$$2$$2$$4$$4$

#### Note:

This is operator "13.7" from ...

9

New Number: 14.4 |  AESZ:  |  Superseeker: 10 13958/9  |  Hash: 0091fcfec3692ae6ced2f585ef96177c

Degree: 14

$3^{6} \theta^4-3^{6} x\theta(15+70\theta+110\theta^2+13\theta^3)-3^{3} x^{2}\left(120409\theta^4+434560\theta^3+542371\theta^2+323352\theta+78624\right)-3^{3} x^{3}\left(5396953\theta^4+22626666\theta^3+37042425\theta^2+28217556\theta+8482968\right)-2 x^{4}\left(1704421489\theta^4+8538160718\theta^3+16779519205\theta^2+14919147216\theta+5077251288\right)-2^{2} 3 x^{5}\left(4201278867\theta^4+24797778110\theta^3+56302322281\theta^2+56325956066\theta+20967103728\right)-2^{3} x^{6}\left(63154319213\theta^4+432278933514\theta^3+1110085421927\theta^2+1224810967950\theta+489654799596\right)-2^{5} 3 x^{7}\left(36597277323\theta^4+286904817870\theta^3+822690934223\theta^2+989019393562\theta+419959932336\right)-2^{6} x^{8}\left(263122045911\theta^4+2344932626130\theta^3+7455815983415\theta^2+9696396501490\theta+4343347545434\right)-2^{7} 5 x^{9}\left(83257168289\theta^4+843955668354\theta^3+2974370084181\theta^2+4174636770342\theta+1965917099796\right)-2^{9} 5 x^{10}\left(38447331387\theta^4+453440983815\theta^3+1797507529325\theta^2+2740147614260\theta+1358896159983\right)-2^{8} 5^{2} 23 x^{11}(\theta+1)(421574469\theta^3+6597293181\theta^2+28022760832\theta+32033938840)+2^{9} 5^{2} 7 23^{2} x^{12}(\theta+2)(\theta+1)(2012137\theta^2+10160979\theta-151326)+2^{10} 5^{3} 7^{2} 23^{3} x^{13}(1525\theta+10484)(\theta+3)(\theta+2)(\theta+1)-2^{11} 3 5^{3} 7^{3} 23^{4} x^{14}(\theta+1)(\theta+2)(\theta+3)(\theta+4)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 182, 7020, 401730, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, 2591/27, 13958/9, 1037839/27, 3535478/3, ... ; Common denominator:...

#### Discriminant

$-(6z+1)(42320z^4+16560z^3+2032z^2+68z-1)(920z^3-1180z^2-378z-27)^2(7z+1)^3$

#### Local exponents

$-\frac{ 1}{ 6}$ ≈$-0.157194$ ≈$-0.157194$ ≈$-0.151128$$-\frac{ 1}{ 7}$ ≈$-0.124614$ ≈$-0.087777$$0$ ≈$0.010861$ ≈$1.55835$$\infty$
$0$$0$$0$$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$1$$1$$0$$1$$1$$0$$1$$1$$2$
$1$$1$$1$$3$$0$$3$$1$$0$$1$$3$$3$
$2$$2$$2$$4$$0$$4$$2$$0$$2$$4$$4$

#### Note:

This is operator "14.4" from ...

10

New Number: 7.20 |  AESZ:  |  Superseeker: 10 3394/3  |  Hash: 9d5791eaabb9d0e9cb4b5cd0b2158b12

Degree: 7

$\theta^4-x\left(88\theta^3-4+71\theta^4+42\theta^2-2\theta\right)-x^{2}\left(10462\theta+13294\theta^2+875\theta^4+6848\theta^3+3132\right)+3^{2} x^{3}\left(373\theta^4-6360\theta^3-30716\theta^2-44868\theta-23180\right)+3^{4} x^{4}\left(1843\theta^4+8384\theta^3+3236\theta^2-14996\theta-15180\right)+3^{8} x^{5}\left(75\theta^4+1272\theta^3+3454\theta^2+3554\theta+1192\right)-3^{11} x^{6}\left(27\theta^4-414\theta^2-918\theta-584\right)-3^{16} x^{7}\left((\theta+2)^4\right)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -4, 147, 4496, 223111, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, 77, 3394/3, 24029, 640402, ... ; Common denominator:...

#### Discriminant

$-(-1+81z)(9z-1)^2(81z^2+14z+1)^2$

#### Local exponents

$-\frac{ 7}{ 81}-\frac{ 4}{ 81}\sqrt{ 2}I$$-\frac{ 7}{ 81}+\frac{ 4}{ 81}\sqrt{ 2}I$$0$$\frac{ 1}{ 81}$$\frac{ 1}{ 9}$$\infty$
$0$$0$$0$$0$$0$$2$
$-\frac{ 1}{ 2}$$-\frac{ 1}{ 2}$$0$$1$$1$$2$
$1$$1$$0$$1$$3$$2$
$\frac{ 3}{ 2}$$\frac{ 3}{ 2}$$0$$2$$4$$2$

#### Note:

This is operator "7.20" from ...

11

New Number: 9.3 |  AESZ:  |  Superseeker: 10 3394/3  |  Hash: 40e3715abcc5c4cb07e700ca79f80abf

Degree: 9

$\theta^4-x\left(57\theta^4+116\theta^3+84\theta^2+26\theta+3\right)-2 x^{2}\left(894\theta^4+3208\theta^3+4571\theta^2+2771\theta+651\right)-2 x^{3}\left(7322\theta^4+56368\theta^3+124783\theta^2+101099\theta+29757\right)+2 3^{2} x^{4}\left(6967\theta^4-27080\theta^3-139991\theta^2-138507\theta-45297\right)+2 3^{4} x^{5}\left(17617\theta^4+49068\theta^3-31255\theta^2-79893\theta-34578\right)+2 3^{8} x^{6}\left(1082\theta^4+8360\theta^3+7967\theta^2+1439\theta-773\right)-2 3^{11} x^{7}\left(198\theta^4-864\theta^3-1545\theta^2-909\theta-155\right)-3^{15} x^{8}\left(69\theta^4+144\theta^3+126\theta^2+54\theta+10\right)-3^{20} x^{9}\left((\theta+1)^4\right)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 3, 135, 5349, 258039, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, 77, 3394/3, 24029, 640402, ... ; Common denominator:...

#### Discriminant

$-(-1+81z)(-1+9z)^2(81z^2+14z+1)^3$

#### Local exponents

$-\frac{ 7}{ 81}-\frac{ 4}{ 81}\sqrt{ 2}I$$-\frac{ 7}{ 81}+\frac{ 4}{ 81}\sqrt{ 2}I$$0$$\frac{ 1}{ 81}$$\frac{ 1}{ 9}$$\infty$
$0$$0$$0$$0$$0$$1$
$\frac{ 1}{ 2}$$\frac{ 1}{ 2}$$0$$1$$1$$1$
$\frac{ 3}{ 2}$$\frac{ 3}{ 2}$$0$$1$$3$$1$
$2$$2$$0$$2$$4$$1$

#### Note:

This is operator "9.3" from ...

12

New Number: 8.87 |  AESZ:  |  Superseeker: 10 18994/9  |  Hash: 038b62cbc5b6e43ac232ededcc3b6a59

Degree: 8

$\theta^4+2 x\theta(-2-13\theta-22\theta^2+88\theta^3)+2^{2} x^{2}\left(3323\theta^4+722\theta^3+2365\theta^2+1306\theta+256\right)+2^{4} 3 x^{3}\left(12903\theta^4+16874\theta^3+21943\theta^2+11164\theta+2164\right)+2^{5} x^{4}\left(618707\theta^4+1367710\theta^3+1570347\theta^2+801712\theta+157652\right)+2^{9} 3 x^{5}\left(248985\theta^4+660583\theta^3+726977\theta^2+362865\theta+69886\right)+2^{11} x^{6}\left(1818051\theta^4+4794576\theta^3+4692593\theta^2+2080392\theta+357884\right)+2^{17} 5 7 x^{7}\left(3223\theta^4+8030\theta^3+8618\theta^2+4603\theta+1002\right)+2^{23} 5^{2} 7^{2} x^{8}\left((\theta+1)^4\right)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, -64, 576, 22716, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, -581/4, 18994/9, -274969/8, 3458142/5, ... ; Common denominator:...

#### Discriminant

$(1+44z+2008z^2+39424z^3+32768z^4)(10z+1)^2(56z+1)^2$

#### Local exponents

$-\frac{ 1}{ 10}$$-\frac{ 1}{ 56}$$0$$s_1$$s_3$$s_2$$s_4$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$0$$1$$1$$1$$1$$1$
$3$$3$$0$$1$$1$$1$$1$$1$
$4$$4$$0$$2$$2$$2$$2$$1$

#### Note:

This is operator "8.87" from ...