Atkin-Lehner |
3+ 7- 11+ 53- |
Signs for the Atkin-Lehner involutions |
Class |
85701g |
Isogeny class |
Conductor |
85701 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
87360 |
Modular degree for the optimal curve |
Δ |
-1062771844827 = -1 · 3 · 73 · 117 · 53 |
Discriminant |
Eigenvalues |
0 3+ 0 7- 11+ -1 8 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-583,-49701] |
[a1,a2,a3,a4,a6] |
Generators |
[586:4343:8] |
Generators of the group modulo torsion |
j |
-64000000000/3098460189 |
j-invariant |
L |
3.8331853012424 |
L(r)(E,1)/r! |
Ω |
0.38289959453405 |
Real period |
R |
5.0054705687092 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999969233 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85701v1 |
Quadratic twists by: -7 |