Atkin-Lehner |
2+ 3+ 5+ 11+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
56760a |
Isogeny class |
Conductor |
56760 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
688128 |
Modular degree for the optimal curve |
Δ |
1374444786008250000 = 24 · 38 · 56 · 117 · 43 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 1 11+ -4 -4 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-325916,44235741] |
[a1,a2,a3,a4,a6] |
Generators |
[-439:10125:1] |
Generators of the group modulo torsion |
j |
239288653920542911744/85902799125515625 |
j-invariant |
L |
4.1976008970805 |
L(r)(E,1)/r! |
Ω |
0.24782265376798 |
Real period |
R |
2.1172403093688 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000053 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
113520p1 |
Quadratic twists by: -4 |