Atkin-Lehner |
2+ 3+ 13+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
72384b |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
49152 |
Modular degree for the optimal curve |
Δ |
68699943936 = 210 · 34 · 134 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ 2 0 0 13+ 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-3357,74925] |
[a1,a2,a3,a4,a6] |
Generators |
[-63:180:1] |
Generators of the group modulo torsion |
j |
4087023572992/67089789 |
j-invariant |
L |
6.1414024803098 |
L(r)(E,1)/r! |
Ω |
1.099617197853 |
Real period |
R |
2.7925183837583 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000174 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72384ct1 9048p1 |
Quadratic twists by: -4 8 |