### Summary

You searched for: sol=60

1

New Number: 2.54 |  AESZ: 41  |  Superseeker: 2 -104  |  Hash: a9ddeed4299f59fb9ac9f6f248383b8f

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 54, 60, -19530, ...
--> OEIS
Normalized instanton numbers (n0=1): 2, -7, -104, -588, 3300, ... ; Common denominator:...

#### Discriminant

$1-56z+1296z^2$

#### Local exponents

$0$$\frac{ 7}{ 324}-\frac{ 1}{ 81}\sqrt{ 2}I$$\frac{ 7}{ 324}+\frac{ 1}{ 81}\sqrt{ 2}I$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$0$$1$$1$$1$
$0$$1$$1$$1$
$0$$2$$2$$\frac{ 3}{ 2}$

#### Note:

Hadamard product $I \ast \delta$

2

New Number: 2.66 |  AESZ:  |  Superseeker: -192 -229568  |  Hash: 0fb32be57a9fcd1b243f9e1341b39d45

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 60, 13860, 4084080, 1338557220, ...
--> OEIS
Normalized instanton numbers (n0=1): -192, 4182, -229568, 19136058, -2006581440, ... ; Common denominator:...

#### Discriminant

$(432z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 432}$$\infty$
$0$$0$$\frac{ 1}{ 6}$
$0$$0$$\frac{ 5}{ 6}$
$0$$1$$\frac{ 7}{ 6}$
$0$$1$$\frac{ 11}{ 6}$

#### Note:

This is operator "2.66" from ...

3

New Number: 5.131 |  AESZ:  |  Superseeker: 325 9106834/3  |  Hash: 79657f8be76c1fed5fd1a658989ca15a

Degree: 5

$\theta^4-x\left(60+460\theta+1565\theta^2+2210\theta^3-623\theta^4\right)-2^{5} 3^{2} x^{2}\left(550\theta^4+2764\theta^3-3581\theta^2-2190\theta-459\right)-2^{8} 3^{4} x^{3}\left(2164\theta^4-17928\theta^3-13315\theta^2-3645\theta-126\right)+2^{14} 3^{8} x^{4}(2\theta+1)(148\theta^3+114\theta^2-35\theta-41)-2^{20} 3^{12} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 60, 5508, 362400, -34621020, ...
--> OEIS
Normalized instanton numbers (n0=1): 325, -24254, 9106834/3, -514805406, 102077718255, ... ; Common denominator:...

#### Discriminant

$-(81z-1)(82944z^2-448z+1)(1+576z)^2$

#### Local exponents

$-\frac{ 1}{ 576}$$0$$\frac{ 7}{ 2592}-\frac{ 1}{ 648}\sqrt{ 2}I$$\frac{ 7}{ 2592}+\frac{ 1}{ 648}\sqrt{ 2}I$$\frac{ 1}{ 81}$$\infty$
$0$$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$0$$1$$1$$1$$1$
$3$$0$$1$$1$$1$$1$
$4$$0$$2$$2$$2$$\frac{ 3}{ 2}$

#### Note:

B-Incarnation as fibre product 62211- x 326--1

4

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 ...

5

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 ...

6

New Number: 7.16 |  AESZ:  |  Superseeker: 22/5 68  |  Hash: 660211ce6175f36772066594bfc33cbb

Degree: 7

$5^{2} \theta^4-2 5 x\theta(15+71\theta+112\theta^2+38\theta^3)-2^{2} x^{2}\left(4364\theta^4+15872\theta^3+24679\theta^2+19360\theta+6000\right)-2^{4} 3^{2} 5 x^{3}\left(92\theta^4+224\theta^3+103\theta^2-176\theta-165\right)+2^{6} 3^{2} x^{4}\left(1228\theta^4+10496\theta^3+30154\theta^2+35736\theta+14715\right)+2^{9} 3^{4} x^{5}(\theta+1)(38\theta^3+74\theta^2-304\theta-495)-2^{10} 3^{4} x^{6}(2\theta+13)(2\theta+3)(17\theta+39)(\theta+1)-2^{12} 3^{6} x^{7}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 60, 480, 16524, ...
--> OEIS
Normalized instanton numbers (n0=1): 22/5, 8, 68, 3292/5, 38826/5, ... ; Common denominator:...

#### Discriminant

$-(-1+36z)(12z+5)^2(12z+1)^2(4z-1)^2$

#### Local exponents

$-\frac{ 5}{ 12}$$-\frac{ 1}{ 12}$$0$$\frac{ 1}{ 36}$$\frac{ 1}{ 4}$$\infty$
$0$$0$$0$$0$$0$$1$
$1$$0$$0$$1$$\frac{ 1}{ 2}$$\frac{ 3}{ 2}$
$3$$1$$0$$1$$\frac{ 1}{ 2}$$\frac{ 5}{ 2}$
$4$$1$$0$$2$$1$$3$

#### Note:

This is operator "7.16" from ...