Atkin-Lehner |
2+ 5+ 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82810q |
Isogeny class |
Conductor |
82810 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
516096 |
Modular degree for the optimal curve |
Δ |
7234654271002340 = 22 · 5 · 78 · 137 |
Discriminant |
Eigenvalues |
2+ -2 5+ 7- -4 13+ 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-49859,-1274934] |
[a1,a2,a3,a4,a6] |
Generators |
[-206:617:1] [-181:1442:1] |
Generators of the group modulo torsion |
j |
24137569/12740 |
j-invariant |
L |
5.1020142506075 |
L(r)(E,1)/r! |
Ω |
0.33900604682882 |
Real period |
R |
1.8812401351502 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999995758 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
11830h1 6370x1 |
Quadratic twists by: -7 13 |