Atkin-Lehner |
2- 3+ 5+ 7+ 41- |
Signs for the Atkin-Lehner involutions |
Class |
8610j |
Isogeny class |
Conductor |
8610 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
7680 |
Modular degree for the optimal curve |
Δ |
-67711795200 = -1 · 220 · 32 · 52 · 7 · 41 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7+ 0 -2 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,1004,3029] |
[a1,a2,a3,a4,a6] |
Generators |
[-1:45:1] |
Generators of the group modulo torsion |
j |
111917452231871/67711795200 |
j-invariant |
L |
4.9875463531834 |
L(r)(E,1)/r! |
Ω |
0.67496173426678 |
Real period |
R |
1.477875292768 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
68880cj1 25830o1 43050t1 60270bq1 |
Quadratic twists by: -4 -3 5 -7 |