### Summary

You searched for: Spectrum0=0,1/6,5/6,1

1

New Number: 2.35 |  AESZ: ~67  |  Superseeker: 480 -16034720  |  Hash: f06ee3928cd6d738db065f3f83d12160

Degree: 2

$\theta^4-2^{4} 3 x(2\theta+1)^2(72\theta^2+72\theta+31)+2^{12} 3^{6} x^{2}(2\theta+1)^2(2\theta+3)^2$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 1488, 5351184, 24363091200, 123873273392400, ...
--> OEIS
Normalized instanton numbers (n0=1): 480, -226968, -16034720, 10943202744, -4352645747040, ... ; Common denominator:...

#### Discriminant

$(6912z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 6912}$$\infty$
$0$$0$$\frac{ 1}{ 2}$
$0$$\frac{ 1}{ 6}$$\frac{ 1}{ 2}$
$0$$\frac{ 5}{ 6}$$\frac{ 3}{ 2}$
$0$$1$$\frac{ 3}{ 2}$

#### Note:

This is operator "2.35" from ...

2

New Number: 2.36 |  AESZ:  |  Superseeker: -36 128217204  |  Hash: 4dbde07f1392f8d49d0e10858d3a17f1

Degree: 2

$\theta^4-2^{2} 3^{2} x(3\theta+1)(3\theta+2)(72\theta^2+72\theta+31)+2^{8} 3^{8} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 2232, 13377960, 102324983040, 875961004703400, ...
--> OEIS
Normalized instanton numbers (n0=1): -36, -486279, 128217204, -74772628524, 63925611915744, ... ; Common denominator:...

#### Discriminant

$(11664z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 11664}$$\infty$
$0$$0$$\frac{ 1}{ 3}$
$0$$\frac{ 1}{ 6}$$\frac{ 2}{ 3}$
$0$$\frac{ 5}{ 6}$$\frac{ 4}{ 3}$
$0$$1$$\frac{ 5}{ 3}$

#### Note:

This is operator "2.36" from ...

3

New Number: 2.37 |  AESZ:  |  Superseeker: -2592 81451104  |  Hash: fb56d2f39692cfb98f66d467355b3c99

Degree: 2

$\theta^4-2^{4} 3 x(4\theta+1)(4\theta+3)(72\theta^2+72\theta+31)+2^{12} 3^{6} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 4464, 62430480, 1125574813440, 22774986122288400, ...
--> OEIS
Normalized instanton numbers (n0=1): -2592, -307800, 81451104, 144135316512, 98667659422368, ... ; Common denominator:...

#### Discriminant

$(27648z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 27648}$$\infty$
$0$$0$$\frac{ 1}{ 4}$
$0$$\frac{ 1}{ 6}$$\frac{ 3}{ 4}$
$0$$\frac{ 5}{ 6}$$\frac{ 5}{ 4}$
$0$$1$$\frac{ 7}{ 4}$

#### Note:

Hadamard product $B\ast c$.

4

New Number: 2.38 |  AESZ: 61  |  Superseeker: -41184 -5124430612320  |  Hash: 191cd9ad5f43862072f3be6811803748

Degree: 2

$\theta^4-2^{4} 3^{2} x(6\theta+1)(6\theta+5)(72\theta^2+72\theta+31)+2^{12} 3^{8} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 22320, 2060205840, 248752033770240, 33839074380496104720, ...
--> OEIS
Normalized instanton numbers (n0=1): -41184, 251271360, -5124430612320, 160031225395327320, -6251395923736354968480, ... ; Common denominator:...

#### Discriminant

$(186624z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 186624}$$\infty$
$0$$0$$\frac{ 1}{ 6}$
$0$$\frac{ 1}{ 6}$$\frac{ 5}{ 6}$
$0$$\frac{ 5}{ 6}$$\frac{ 7}{ 6}$
$0$$1$$\frac{ 11}{ 6}$

#### Note:

This is operator "2.38" from ...

5

New Number: 2.58 |  AESZ: 46  |  Superseeker: -6 -104  |  Hash: 2226ec115674e71c483ba2c0350e8adf

Degree: 2

$\theta^4-2 3 x(2\theta+1)^2(9\theta^2+9\theta+5)+2^{2} 3^{6} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 30, 1782, 129900, 10463670, ...
--> OEIS
Normalized instanton numbers (n0=1): -6, -6, -104, 36, -4812, ... ; Common denominator:...

#### Discriminant

$(108z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 108}$$\infty$
$0$$0$$\frac{ 1}{ 2}$
$0$$\frac{ 1}{ 6}$$1$
$0$$\frac{ 5}{ 6}$$1$
$0$$1$$\frac{ 3}{ 2}$

#### Note:

Hadamard product $I \ast \iota$

6

New Number: 3.15 |  AESZ:  |  Superseeker: -32 -16288  |  Hash: e21c92d8f9a2222be40fdc71ea51ee35

Degree: 3

$\theta^4+2^{3} x\left(21\theta^4+42\theta^3+30\theta^2+9\theta+1\right)-2^{6} x^{2}(\theta+1)^2(96\theta^2+192\theta+77)+2^{9} 5^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -8, 720, -68480, 8123920, ...
--> OEIS
Normalized instanton numbers (n0=1): -32, 468, -16288, 1681645/2, -53608288, ... ; Common denominator:...

#### Discriminant

$(200z+1)(-1+16z)^2$

#### Local exponents

$-\frac{ 1}{ 200}$$0$$\frac{ 1}{ 16}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$1$$0$$\frac{ 1}{ 6}$$1$
$1$$0$$\frac{ 5}{ 6}$$2$
$2$$0$$1$$\frac{ 5}{ 2}$

#### Note:

Operator equivalent to AESZ 328

7

New Number: 3.20 |  AESZ: 390  |  Superseeker: 19 4455  |  Hash: cd8ca8746f3610e70893770a090533f9

Degree: 3

$\theta^4-x\left(561\theta^4+1122\theta^3+975\theta^2+414\theta+70\right)+2^{2} 7^{2} x^{2}(\theta+1)^2(534\theta^2+1068\theta+433)-2^{2} 7^{4} 13^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 70, 8442, 1192660, 182057050, ...
--> OEIS
Normalized instanton numbers (n0=1): 19, -276, 4455, -104648, 2969383, ... ; Common denominator:...

#### Discriminant

$-(169z-1)(-1+196z)^2$

#### Local exponents

$0$$\frac{ 1}{ 196}$$\frac{ 1}{ 169}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$0$$\frac{ 1}{ 6}$$1$$1$
$0$$\frac{ 5}{ 6}$$1$$2$
$0$$1$$2$$\frac{ 5}{ 2}$

#### Note:

This is operator "3.20" from ...

8

New Number: 5.65 |  AESZ: 273  |  Superseeker: 63/5 14016/5  |  Hash: cf49bc645cb0404ce7bc9ca1d41d3152

Degree: 5

$5^{2} \theta^4-3 5 x\left(333\theta^4+882\theta^3+781\theta^2+340\theta+60\right)+2^{2} 3^{2} x^{2}\left(5184\theta^4+40662\theta^3+71829\theta^2+47700\theta+11540\right)+2^{2} 3^{5} x^{3}\left(8424\theta^4+9720\theta^3-46899\theta^2-63045\theta-21260\right)-2^{4} 3^{8} x^{4}\left(1296\theta^4+12312\theta^3+23094\theta^2+16263\theta+3956\right)-2^{6} 3^{11} x^{5}(3\theta+2)(3\theta+4)(6\theta+5)(6\theta+7)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 36, 2196, 161280, 13032900, ...
--> OEIS
Normalized instanton numbers (n0=1): 63/5, -747/4, 14016/5, -55584, 6071598/5, ... ; Common denominator:...

#### Discriminant

$-(-1+27z)(108z+5)^2(108z-1)^2$

#### Local exponents

$-\frac{ 5}{ 108}$$0$$\frac{ 1}{ 108}$$\frac{ 1}{ 27}$$\infty$
$0$$0$$0$$0$$\frac{ 2}{ 3}$
$1$$0$$\frac{ 1}{ 6}$$1$$\frac{ 5}{ 6}$
$3$$0$$\frac{ 5}{ 6}$$1$$\frac{ 7}{ 6}$
$4$$0$$1$$2$$\frac{ 4}{ 3}$

#### Note:

This is operator "5.65" from ...

9

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 ...

10

New Number: 8.71 |  AESZ:  |  Superseeker: -15 14044/3  |  Hash: de469dbb89801caa07ec523e3b0e4772

Degree: 8

$\theta^4+3 x\left(111\theta^4+186\theta^3+169\theta^2+76\theta+14\right)+2 3^{2} x^{2}\left(2529\theta^4+6930\theta^3+9483\theta^2+6096\theta+1508\right)+2^{2} 3^{4} x^{3}\left(11367\theta^4+32886\theta^3+47658\theta^2+36099\theta+10084\right)+2^{3} 3^{6} x^{4}\left(37017\theta^4+100278\theta^3+103626\theta^2+56025\theta+11582\right)+2^{4} 3^{9} x^{5}\left(29160\theta^4+80676\theta^3+84897\theta^2+27261\theta-568\right)+2^{5} 3^{12} x^{6}\left(16200\theta^4+40824\theta^3+53991\theta^2+31131\theta+6578\right)+2^{7} 3^{17} x^{7}\left(360\theta^4+936\theta^3+1056\theta^2+585\theta+131\right)+2^{9} 3^{20} x^{8}(\theta+1)^2(6\theta+5)(6\theta+7)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -42, 2682, -200436, 16310250, ...
--> OEIS
Normalized instanton numbers (n0=1): -15, 39, 14044/3, 213069/2, 462576, ... ; Common denominator:...

#### Discriminant

$(27z+1)(54z+1)(108z+1)^2(1944z^2+18z+1)^2$

#### Local exponents

$-\frac{ 1}{ 27}$$-\frac{ 1}{ 54}$$-\frac{ 1}{ 108}$$-\frac{ 1}{ 216}-\frac{ 1}{ 216}\sqrt{ 23}I$$-\frac{ 1}{ 216}+\frac{ 1}{ 216}\sqrt{ 23}I$$0$$\infty$
$0$$0$$0$$0$$0$$0$$\frac{ 5}{ 6}$
$1$$1$$\frac{ 1}{ 6}$$1$$1$$0$$1$
$1$$1$$\frac{ 5}{ 6}$$3$$3$$0$$1$
$2$$2$$1$$4$$4$$0$$\frac{ 7}{ 6}$

#### Note:

This is operator "8.71" from ...