Atkin-Lehner |
2+ 3+ 5+ 71+ |
Signs for the Atkin-Lehner involutions |
Class |
68160b |
Isogeny class |
Conductor |
68160 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
49152 |
Modular degree for the optimal curve |
Δ |
-16751001600 = -1 · 220 · 32 · 52 · 71 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 2 -2 6 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,639,-639] |
[a1,a2,a3,a4,a6] |
Generators |
[3:36:1] |
Generators of the group modulo torsion |
j |
109902239/63900 |
j-invariant |
L |
5.9253050170365 |
L(r)(E,1)/r! |
Ω |
0.73072765262424 |
Real period |
R |
2.0271933722564 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999995597 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68160cy1 2130m1 |
Quadratic twists by: -4 8 |