Atkin-Lehner |
2- 3+ 5+ 7+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
84420a |
Isogeny class |
Conductor |
84420 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
253440 |
Modular degree for the optimal curve |
Δ |
132565781250000 = 24 · 33 · 510 · 7 · 672 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7+ 0 -4 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-34548,-2408747] |
[a1,a2,a3,a4,a6] |
Generators |
[34692:752209:64] |
Generators of the group modulo torsion |
j |
10556226451095552/306865234375 |
j-invariant |
L |
5.0133056054726 |
L(r)(E,1)/r! |
Ω |
0.35080489931355 |
Real period |
R |
7.1454327169065 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999917428 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
84420e1 |
Quadratic twists by: -3 |