Summary

You searched for: h3=7

Your search produced 2 matches

You can download all data as plain text or as JSON

1

New Number: 3.22 |  AESZ: 392  |  Superseeker: 166 1016100  |  Hash: 5862be5cc4d3ec1686e6b9a6ec08f7e7  

Degree: 3

\(\theta^4-2 x\left(230\theta^4+496\theta^3+323\theta^2+75\theta+6\right)-2^{2} 3 x^{2}(6\theta+5)(1866\theta^3+5341\theta^2+4760\theta+1084)-2^{4} 3^{2} 13^{2} x^{3}(6\theta+5)(6\theta+11)(3\theta+1)(3\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 5760, 1664544, 681014880, ...
--> OEIS
Normalized instanton numbers (n0=1): 166, 8076, 1016100, 189329096, 43879949258, ... ; Common denominator:...

Discriminant

\(-(676z-1)(1+108z)^2\)

Local exponents

\(-\frac{ 1}{ 108}\)\(0\)\(\frac{ 1}{ 676}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(\frac{ 1}{ 3}\)\(0\)\(1\)\(\frac{ 5}{ 6}\)
\(1\)\(0\)\(1\)\(\frac{ 11}{ 6}\)
\(\frac{ 4}{ 3}\)\(0\)\(2\)\(\frac{ 7}{ 3}\)

Note:

This is operator "3.22" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

2

New Number: 4.36 |  AESZ: 109  |  Superseeker: 1434/7 18676572/7  |  Hash: bca2938ac7fa09f5bdc395cab75caf82  

Degree: 4

\(7^{2} \theta^4-2 3 7 x\left(1272\theta^4+2508\theta^3+1779\theta^2+525\theta+56\right)+2^{2} 3 x^{2}\left(43704\theta^4+38088\theta^3-25757\theta^2-20608\theta-3360\right)-2^{4} 3^{3} x^{3}\left(2736\theta^4-1512\theta^3-1672\theta^2-357\theta-14\right)-2^{6} 3^{5} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 15840, 8148000, 5126536800, ...
--> OEIS
Normalized instanton numbers (n0=1): 1434/7, 14718, 18676572/7, 4988009280/7, 1646787631350/7, ... ; Common denominator:...

Discriminant

\(-(432z^2+1080z-1)(-7+36z)^2\)

Local exponents

\(-\frac{ 5}{ 4}-\frac{ 13}{ 18}\sqrt{ 3}\)\(0\)\(s_1\)\(s_2\)\(-\frac{ 5}{ 4}+\frac{ 13}{ 18}\sqrt{ 3}\)\(\frac{ 7}{ 36}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(2\)\(2\)\(4\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex