Atkin-Lehner |
2- 7+ 73- |
Signs for the Atkin-Lehner involutions |
Class |
57232d |
Isogeny class |
Conductor |
57232 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1354752 |
Modular degree for the optimal curve |
Δ |
-220636367028224 = -1 · 219 · 78 · 73 |
Discriminant |
Eigenvalues |
2- -1 3 7+ 0 -1 6 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-11747864,-15494470928] |
[a1,a2,a3,a4,a6] |
Generators |
[678075741108186558530529540:-1075113640515858844845048896:171265616185327844300875] |
Generators of the group modulo torsion |
j |
-7593748539095257/9344 |
j-invariant |
L |
6.8099837220912 |
L(r)(E,1)/r! |
Ω |
0.040773672317945 |
Real period |
R |
41.754785226287 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7154c1 57232k1 |
Quadratic twists by: -4 -7 |