### Summary

You searched for: inst=1

1

New Number: 2.64 |  AESZ: 182  |  Superseeker: 1 7  |  Hash: 89ba4729efa82413b33fe6928ff8d2c9

Degree: 2

$\theta^4-x\left(43\theta^4+86\theta^3+77\theta^2+34\theta+6\right)+2^{2} 3 x^{2}(\theta+1)^2(6\theta+5)(6\theta+7)$

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Coefficients of the holomorphic solution: 1, 6, 66, 924, 14850, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, 7/4, 7, 40, 270, ... ; Common denominator:...

#### Discriminant

$(27z-1)(16z-1)$

#### Local exponents

$0$$\frac{ 1}{ 27}$$\frac{ 1}{ 16}$$\infty$
$0$$0$$0$$\frac{ 5}{ 6}$
$0$$1$$1$$1$
$0$$1$$1$$1$
$0$$2$$2$$\frac{ 7}{ 6}$

#### Note:

This is operator "2.64" from ...

2

New Number: 2.69 |  AESZ: 205  |  Superseeker: 1 5  |  Hash: 4fb2e7002e630237d0458c3985cd6a18

Degree: 2

$\theta^4-x\left(59\theta^4+118\theta^3+105\theta^2+46\theta+8\right)+2^{5} 3 x^{2}(\theta+1)^2(3\theta+2)(3\theta+4)$

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Coefficients of the holomorphic solution: 1, 8, 120, 2240, 46840, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, 7/4, 5, 24, 759/5, ... ; Common denominator:...

#### Discriminant

$(32z-1)(27z-1)$

#### Local exponents

$0$$\frac{ 1}{ 32}$$\frac{ 1}{ 27}$$\infty$
$0$$0$$0$$\frac{ 2}{ 3}$
$0$$1$$1$$1$
$0$$1$$1$$1$
$0$$2$$2$$\frac{ 4}{ 3}$

#### Note:

This is operator "2.69" from ...

3

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$

4

New Number: 4.77 |  AESZ:  |  Superseeker: 1 68/9  |  Hash: f9623221ffe8be4c1e31a6e6ce195a37

Degree: 4

$\theta^4-x\left(16+80\theta+161\theta^2+162\theta^3+81\theta^4\right)+2^{3} x^{2}\left(303\theta^4+1212\theta^3+1952\theta^2+1480\theta+440\right)-2^{6} x^{3}(124\theta^2+372\theta+263)(2\theta+3)^2+2^{9} 3 5^{2} x^{4}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 280, 5152, 98200, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, -2, 68/9, -30, 150, ... ; Common denominator:...

#### Discriminant

$(25z-1)(24z-1)(-1+16z)^2$

#### Local exponents

$0$$\frac{ 1}{ 25}$$\frac{ 1}{ 24}$$\frac{ 1}{ 16}$$\infty$
$0$$0$$0$$0$$1$
$0$$1$$1$$\frac{ 1}{ 2}$$\frac{ 3}{ 2}$
$0$$1$$1$$\frac{ 1}{ 2}$$\frac{ 5}{ 2}$
$0$$2$$2$$1$$3$

#### Note:

B-Incarnation: SII4411

5

New Number: 5.102 |  AESZ: 352  |  Superseeker: 1 -12  |  Hash: fc8b141522720827b1dd2cd28a232c1b

Degree: 5

$\theta^4-x\left(70\theta^4+86\theta^3+77\theta^2+34\theta+6\right)+3 x^{2}\left(675\theta^4+1602\theta^3+1933\theta^2+1130\theta+258\right)-2^{2} 3^{3} x^{3}\left(271\theta^4+888\theta^3+1259\theta^2+831\theta+207\right)+2^{2} 3^{5} x^{4}\left(212\theta^4+808\theta^3+1189\theta^2+773\theta+186\right)-2^{4} 3^{7} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 54, 492, 3510, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, -7/8, -12, -131/4, 90, ... ; Common denominator:...

#### Discriminant

$-(16z-1)(432z^2-36z+1)(-1+9z)^2$

#### Local exponents

$0$$\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I$$\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I$$\frac{ 1}{ 16}$$\frac{ 1}{ 9}$$\infty$
$0$$0$$0$$0$$0$$\frac{ 3}{ 4}$
$0$$1$$1$$1$$1$$1$
$0$$1$$1$$1$$3$$1$
$0$$2$$2$$2$$4$$\frac{ 5}{ 4}$

#### Note:

This is operator "5.102" from ...

6

New Number: 5.93 |  AESZ: 333  |  Superseeker: 1 2668/3  |  Hash: dc274781605ee4262d8745e3fa3a8057

Degree: 5

$\theta^4+x\theta^2(71\theta^2-2\theta-1)+2^{3} 3 x^{2}\left(154\theta^4+334\theta^3+461\theta^2+248\theta+48\right)+2^{6} 3^{2} x^{3}(5\theta+3)(31\theta^3+39\theta^2-25\theta-21)+2^{9} 3^{4} x^{4}(2\theta+1)(2\theta^3-33\theta^2-56\theta-24)-2^{12} 3^{6} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, -72, 1440, 22680, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, -66, 2668/3, -2774, -167786, ... ; Common denominator:...

#### Discriminant

$-(9z-1)(2304z^2+32z+1)(1+24z)^2$

#### Local exponents

$-\frac{ 1}{ 24}$$-\frac{ 1}{ 144}-\frac{ 1}{ 72}\sqrt{ 2}I$$-\frac{ 1}{ 144}+\frac{ 1}{ 72}\sqrt{ 2}I$$0$$\frac{ 1}{ 9}$$\infty$
$0$$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$1$$1$$0$$1$$1$
$3$$1$$1$$0$$1$$1$
$4$$2$$2$$0$$2$$\frac{ 3}{ 2}$

#### Note:

This is operator "5.93" from ...

7

New Number: 6.21 |  AESZ:  |  Superseeker: 1 11  |  Hash: 319d6b2f1541de5252840442cc6f8dcd

Degree: 6

$\theta^4+x\left(6+27\theta+47\theta^2+40\theta^3+20\theta^4\right)-x^{2}(143\theta^2+286\theta+120)(\theta+1)^2-2 3^{2} x^{3}(\theta+2)(\theta+1)(291\theta^2+873\theta+766)-2^{2} 3^{3} 5 x^{4}(\theta+3)(\theta+1)(41\theta^2+164\theta+196)+2^{3} 3^{3} 5^{2} x^{5}(\theta+4)(\theta+1)(29\theta^2+145\theta+150)+2^{5} 3^{5} 5^{3} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -6, 60, -480, 5040, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, 13/4, 11, 50, 1674/5, ... ; Common denominator:...

#### Discriminant

$(6z-1)(15z-1)(9z+1)(12z+1)(10z+1)^2$

#### Local exponents

$-\frac{ 1}{ 9}$$-\frac{ 1}{ 10}$$-\frac{ 1}{ 12}$$0$$\frac{ 1}{ 15}$$\frac{ 1}{ 6}$$\infty$
$0$$0$$0$$0$$0$$0$$1$
$1$$\frac{ 1}{ 2}$$1$$0$$1$$1$$2$
$1$$\frac{ 1}{ 2}$$1$$0$$1$$1$$4$
$2$$1$$2$$0$$2$$2$$5$

#### Note:

This is operator "6.21" from ...

8

New Number: 7.10 |  AESZ:  |  Superseeker: 1 11  |  Hash: b1c277f62ba740f9f7e0371ba53e4194

Degree: 7

$\theta^4-x\left(76\theta^4+80\theta^3+73\theta^2+33\theta+6\right)+x^{2}\left(2209\theta^4+4228\theta^3+4745\theta^2+2726\theta+648\right)-2 3^{2} x^{3}\left(1735\theta^4+4646\theta^3+6099\theta^2+4072\theta+1124\right)+2^{2} 3^{3} x^{4}\left(2085\theta^4+7388\theta^3+11695\theta^2+9140\theta+2844\right)-2^{3} 3^{3} x^{5}(\theta+1)(3707\theta^3+14055\theta^2+20242\theta+10704)+2^{6} 3^{5} x^{6}(\theta+1)(\theta+2)(86\theta^2+285\theta+262)-2^{7} 3^{8} x^{7}(\theta+1)(\theta+2)^2(\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 60, 816, 13104, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, 13/4, 11, 50, 1674/5, ... ; Common denominator:...

#### Discriminant

$-(3z-1)(18z-1)(27z-1)(12z-1)^2(-1+2z)^2$

#### Local exponents

$0$$\frac{ 1}{ 27}$$\frac{ 1}{ 18}$$\frac{ 1}{ 12}$$\frac{ 1}{ 3}$$\frac{ 1}{ 2}$$\infty$
$0$$0$$0$$0$$0$$0$$1$
$0$$1$$1$$1$$1$$\frac{ 1}{ 2}$$2$
$0$$1$$1$$3$$1$$\frac{ 1}{ 2}$$2$
$0$$2$$2$$4$$2$$1$$3$

#### Note:

This is operator "7.10" from ...

9

New Number: 8.55 |  AESZ:  |  Superseeker: 1 68/9  |  Hash: 39ed8ce7572bc79a333f77c892033bcf

Degree: 8

$\theta^4-x\left(33\theta^4+98\theta^3+105\theta^2+56\theta+12\right)+2^{3} x^{2}\left(34\theta^4+276\theta^3+609\theta^2+582\theta+216\right)+2^{4} 3 x^{3}\left(11\theta^4-170\theta^3-941\theta^2-1520\theta-846\right)-2^{7} 3^{2} x^{4}(2\theta^2+6\theta+5)(4\theta^2+12\theta-31)+2^{8} 3 x^{5}\left(11\theta^4+302\theta^3+1183\theta^2+1652\theta+726\right)+2^{11} x^{6}\left(34\theta^4+132\theta^3-39\theta^2-708\theta-747\right)-2^{12} x^{7}\left(33\theta^4+298\theta^3+1005\theta^2+1492\theta+816\right)+2^{16} x^{8}\left((\theta+3)^4\right)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 120, 1216, 13080, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, -2, 68/9, -30, 150, ... ; Common denominator:...

#### Discriminant

$(z-1)(16z-1)(16z^2-16z+1)(4z-1)^2(4z+1)^2$

#### Local exponents

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

#### Note:

This is operator "8.55" from ...