Atkin-Lehner |
2- 3+ 23- 61- |
Signs for the Atkin-Lehner involutions |
Class |
67344q |
Isogeny class |
Conductor |
67344 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
28800 |
Modular degree for the optimal curve |
Δ |
-1709998848 = -1 · 28 · 32 · 233 · 61 |
Discriminant |
Eigenvalues |
2- 3+ -2 -1 1 -5 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-69,2025] |
[a1,a2,a3,a4,a6] |
Generators |
[-7:46:1] [0:45:1] |
Generators of the group modulo torsion |
j |
-143982592/6679683 |
j-invariant |
L |
7.7066042912386 |
L(r)(E,1)/r! |
Ω |
1.239181977487 |
Real period |
R |
0.51825884812465 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16836c1 |
Quadratic twists by: -4 |