### Summary

You searched for: inst=879

1

New Number: 5.3 |  AESZ: 20  |  Superseeker: 3 245/3  |  Hash: a9a698dc5c79ffda497a7897390408b0

Degree: 5

$\theta^4-3 x\left(48\theta^4+60\theta^3+53\theta^2+23\theta+4\right)+3^{2} x^{2}\left(873\theta^4+1980\theta^3+2319\theta^2+1344\theta+304\right)-2 3^{4} x^{3}\left(1269\theta^4+3888\theta^3+5259\theta^2+3348\theta+800\right)+2^{2} 3^{6} x^{4}\left(891\theta^4+3240\theta^3+4653\theta^2+2952\theta+688\right)-2^{3} 3^{11} x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 252, 6600, 198540, ...
--> OEIS
Normalized instanton numbers (n0=1): 3, 33/2, 245/3, 879, 11829, ... ; Common denominator:...

#### Discriminant

$-(54z-1)(27z-1)^2(18z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 54}$$\frac{ 1}{ 27}$$\frac{ 1}{ 18}$$\infty$
$0$$0$$0$$0$$\frac{ 2}{ 3}$
$0$$1$$\frac{ 1}{ 3}$$1$$1$
$0$$1$$\frac{ 2}{ 3}$$3$$1$
$0$$2$$1$$4$$\frac{ 4}{ 3}$

#### Note:

A-Incarnation: (3,0),(0,3),(1,1) intersection in $P^3 \times \P^3$.

2

New Number: 7.9 |  AESZ:  |  Superseeker: -3 -245/3  |  Hash: 5641c09b76662b0741e41b41b0c6f105

Degree: 7

$\theta^4-3 x\left(96\theta^4+120\theta^3+127\theta^2+67\theta+14\right)+3^{2} x^{2}\left(3897\theta^4+9540\theta^3+13209\theta^2+9246\theta+2608\right)-2 3^{4} x^{3}\left(14445\theta^4+52002\theta^3+88179\theta^2+73278\theta+23920\right)+2^{2} 3^{6} x^{4}\left(31671\theta^4+149364\theta^3+298089\theta^2+280512\theta+100780\right)-2^{3} 3^{12} x^{5}(\theta+1)(507\theta^3+2439\theta^2+4306\theta+2704)+2^{6} 3^{14} x^{6}(\theta+1)(\theta+2)(90\theta^2+351\theta+370)-2^{7} 3^{19} x^{7}(\theta+1)(\theta+2)^2(\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 42, 1872, 86712, 4126716, ...
--> OEIS
Normalized instanton numbers (n0=1): -3, 69/4, -245/3, 879, -11829, ... ; Common denominator:...

#### Discriminant

$-(36z-1)^2(27z-1)^2(54z-1)^3$

#### Local exponents

$0$$\frac{ 1}{ 54}$$\frac{ 1}{ 36}$$\frac{ 1}{ 27}$$\infty$
$0$$0$$0$$0$$1$
$0$$0$$1$$\frac{ 1}{ 3}$$2$
$0$$-\frac{ 1}{ 3}$$3$$\frac{ 2}{ 3}$$2$
$0$$\frac{ 1}{ 3}$$4$$1$$3$

#### Note:

This is operator "7.9" from ...