Atkin-Lehner |
5+ 37- 89- |
Signs for the Atkin-Lehner involutions |
Class |
82325f |
Isogeny class |
Conductor |
82325 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
1226880 |
Modular degree for the optimal curve |
Δ |
687884063720703125 = 516 · 373 · 89 |
Discriminant |
Eigenvalues |
0 2 5+ -2 5 -1 0 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-1602133,780055043] |
[a1,a2,a3,a4,a6] |
Generators |
[201:21589:1] |
Generators of the group modulo torsion |
j |
29107148052534132736/44024580078125 |
j-invariant |
L |
7.5533263493332 |
L(r)(E,1)/r! |
Ω |
0.2862261830809 |
Real period |
R |
4.3982269930509 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002737 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16465d1 |
Quadratic twists by: 5 |