Atkin-Lehner |
3+ 5+ 7+ 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
75075b |
Isogeny class |
Conductor |
75075 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
811008 |
Modular degree for the optimal curve |
Δ |
326838777890625 = 38 · 57 · 73 · 11 · 132 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 7+ 11+ 13+ -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-1661188,-824784844] |
[a1,a2,a3,a4,a6] |
Generators |
[20502560:1950487284:2197] |
Generators of the group modulo torsion |
j |
32445917389944971641/20917681785 |
j-invariant |
L |
2.80359514922 |
L(r)(E,1)/r! |
Ω |
0.13298261654577 |
Real period |
R |
10.541209146976 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004915 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
15015w1 |
Quadratic twists by: 5 |