### Summary

You searched for: inst=-2

1

New Number: 3.24 |  AESZ:  |  Superseeker: -2 -108  |  Hash: 3c89cc2017daa2eba88c016b8ae5865c

Degree: 3

$\theta^4+2 x(2\theta+1)^2(3\theta^2+3\theta+1)-2^{2} x^{2}(2\theta+1)(2\theta+3)(47\theta^2+94\theta+51)+2^{4} 7 x^{3}(2\theta+1)(2\theta+3)^2(2\theta+5)$

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Coefficients of the holomorphic solution: 1, -2, 54, -980, 26950, ...
--> OEIS
Normalized instanton numbers (n0=1): -2, 17, -108, 1498, -19630, ... ; Common denominator:...

#### Discriminant

$(16z-1)(112z^2-40z-1)$

#### Local exponents

$\frac{ 5}{ 28}-\frac{ 1}{ 7}\sqrt{ 2}$$0$$\frac{ 1}{ 16}$$\frac{ 5}{ 28}+\frac{ 1}{ 7}\sqrt{ 2}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$0$$1$$1$$\frac{ 3}{ 2}$
$1$$0$$1$$1$$\frac{ 3}{ 2}$
$2$$0$$2$$2$$\frac{ 5}{ 2}$

#### Note:

This is operator $\tilde{C_9}$

2

New Number: 3.25 |  AESZ:  |  Superseeker: -2 -308/3  |  Hash: 287da3a26b0da679d81da411b46958d1

Degree: 3

$\theta^4+2 x(2\theta+1)^2(7\theta^2+7\theta+3)+2^{2} x^{2}(2\theta+1)(2\theta+3)(29\theta^2+58\theta+33)+2^{4} 3 5 x^{3}(2\theta+1)(2\theta+3)^2(2\theta+5)$

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Coefficients of the holomorphic solution: 1, -6, 90, -2100, 59850, ...
--> OEIS
Normalized instanton numbers (n0=1): -2, 12, -308/3, 1058, -71158/5, ... ; Common denominator:...

#### Discriminant

$(48z+1)(80z^2+8z+1)$

#### Local exponents

$-\frac{ 1}{ 20}-\frac{ 1}{ 10}I$$-\frac{ 1}{ 20}+\frac{ 1}{ 10}I$$-\frac{ 1}{ 48}$$0$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$1$$1$$0$$\frac{ 3}{ 2}$
$1$$1$$1$$0$$\frac{ 3}{ 2}$
$2$$2$$2$$0$$\frac{ 5}{ 2}$

#### Note:

This is operator $\tilde{C_17}$

3

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

Degree: 4

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

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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

4

New Number: 5.26 |  AESZ: 199  |  Superseeker: -2 3820/9  |  Hash: f7b5c9e3ad50b0885d03c98d07a051f1

Degree: 5

$\theta^4-x\left(15+88\theta+200\theta^2+224\theta^3+265\theta^4\right)+2 3 x^{2}\left(4325\theta^4+6386\theta^3+6011\theta^2+2718\theta+468\right)-2 3^{2} x^{3}\left(62015\theta^4+116478\theta^3+102361\theta^2+37422\theta+4824\right)+3^{6} 17 x^{4}\left(1465\theta^4+3092\theta^3+2686\theta^2+1140\theta+200\right)-3^{10} 17^{2} x^{5}\left((\theta+1)^4\right)$

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Coefficients of the holomorphic solution: 1, 15, 567, 28113, 1584279, ...
--> OEIS
Normalized instanton numbers (n0=1): -2, 28, 3820/9, 3924, 21606, ... ; Common denominator:...

#### Discriminant

$-(z-1)(81z-1)^2(51z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 81}$$\frac{ 1}{ 51}$$1$$\infty$
$0$$0$$0$$0$$1$
$0$$\frac{ 1}{ 2}$$1$$1$$1$
$0$$\frac{ 1}{ 2}$$3$$1$$1$
$0$$1$$4$$2$$1$

#### Note:

There is a second MUM-point at infinity, corresponding to
Operator AESZ 194/5.23.

5

New Number: 6.1 |  AESZ:  |  Superseeker: -2 -70/3  |  Hash: 28ce9053a8969d292554c4f160bc469e

Degree: 6

$\theta^4-x\left(112\theta^4+224\theta^3+280\theta^2+168\theta+39\right)+3 x^{2}\left(1568\theta^4+6272\theta^3+11538\theta^2+10532\theta+3923\right)-2^{3} x^{3}\left(11552\theta^4+69312\theta^3+172218\theta^2+204750\theta+96687\right)+x^{4}\left(872704\theta^4+6981632\theta^3+21940576\theta^2+31909248\theta+18039321\right)-2^{7} 3^{2} x^{5}(784\theta^2+3920\theta+5547)(2\theta+5)^2+2^{14} 3^{4} x^{6}(2\theta+5)(2\theta+7)(\theta+3)^2$

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Coefficients of the holomorphic solution: 1, 39, 2541/2, 80689/2, 10329363/8, ...
--> OEIS
Normalized instanton numbers (n0=1): -2, -9/2, -70/3, -145, -1060, ... ; Common denominator:...

#### Discriminant

$(4z-1)^2(36z-1)^2(16z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 36}$$\frac{ 1}{ 16}$$\frac{ 1}{ 4}$$\infty$
$0$$0$$0$$0$$\frac{ 5}{ 2}$
$0$$-\frac{ 1}{ 2}$$-\frac{ 1}{ 2}$$-\frac{ 1}{ 2}$$3$
$0$$1$$1$$1$$3$
$0$$\frac{ 3}{ 2}$$\frac{ 3}{ 2}$$\frac{ 3}{ 2}$$\frac{ 7}{ 2}$

#### Note:

YY-pullback of AESZ:130

6

New Number: 6.20 |  AESZ:  |  Superseeker: 0 -1/3  |  Hash: 5169c67af7361bf7e6467dabea9612bd

Degree: 6

$\theta^4+x\left(11\theta+26\theta^3+2+13\theta^4+24\theta^2\right)-x^{2}(141\theta^2+282\theta+296)(\theta+1)^2-2 x^{3}(\theta+2)(\theta+1)(407\theta^2+1221\theta+654)+2^{2} 7 x^{4}(\theta+3)(\theta+1)(389\theta^2+1556\theta+1460)-2^{3} 3 7^{2} x^{5}(\theta+4)(\theta+1)(29\theta^2+145\theta+166)+2^{5} 3 7^{3} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)$

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Coefficients of the holomorphic solution: 1, -2, 28, -224, 2464, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, 1/2, -1/3, -1, -2, ... ; Common denominator:...

#### Discriminant

$(-1+2z)(4z-1)(21z^2-9z+1)(1+14z)^2$

#### Local exponents

$-\frac{ 1}{ 14}$$0$$\frac{ 3}{ 14}-\frac{ 1}{ 42}\sqrt{ 3}I$$\frac{ 3}{ 14}+\frac{ 1}{ 42}\sqrt{ 3}I$$\frac{ 1}{ 4}$$\frac{ 1}{ 2}$$\infty$
$0$$0$$0$$0$$0$$0$$1$
$\frac{ 1}{ 2}$$0$$1$$1$$1$$1$$2$
$\frac{ 1}{ 2}$$0$$1$$1$$1$$1$$4$
$1$$0$$2$$2$$2$$2$$5$

#### Note:

This is operator "6.20" from ...

7

New Number: 7.15 |  AESZ:  |  Superseeker: -2 -952  |  Hash: d9a911258d890c112974a4ba19e93e6d

Degree: 7

$\theta^4+2 x\left(138\theta^4+156\theta^3+137\theta^2+59\theta+10\right)+2^{2} x^{2}\left(4796\theta^4+15824\theta^3+16719\theta^2+7610\theta+1400\right)-2^{4} 5 x^{3}\left(5876\theta^4-28824\theta^3-58439\theta^2-39075\theta-9350\right)-2^{6} 5 x^{4}\left(184592\theta^4+414976\theta^3-60816\theta^2-180968\theta-60145\right)+2^{10} 3 x^{5}\left(240624\theta^4-905760\theta^3-1250920\theta^2-576920\theta-83925\right)+2^{18} 3^{2} x^{6}\left(13608\theta^4+48276\theta^3+66402\theta^2+41679\theta+9935\right)-2^{20} 3^{5} x^{7}(6\theta+5)^2(6\theta+7)^2$

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Coefficients of the holomorphic solution: 1, -20, 900, -55280, 3962500, ...
--> OEIS
Normalized instanton numbers (n0=1): -2, -343/2, -952, -45148, -17303644/25, ... ; Common denominator:...

#### Discriminant

$-(-1-16z+256z^2)(32z-1)^2(108z+1)^3$

#### Local exponents

$\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}$$-\frac{ 1}{ 108}$$0$$\frac{ 1}{ 32}$$\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}$$\infty$
$0$$0$$0$$0$$0$$\frac{ 5}{ 6}$
$1$$\frac{ 1}{ 2}$$0$$1$$1$$\frac{ 5}{ 6}$
$1$$\frac{ 3}{ 2}$$0$$3$$1$$\frac{ 7}{ 6}$
$2$$2$$0$$4$$2$$\frac{ 7}{ 6}$

#### Note:

This is operator "7.15" from ...

8

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 ...

9

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 ...