Atkin-Lehner |
2+ 3+ 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368b |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
55296 |
Modular degree for the optimal curve |
Δ |
2882221056 = 210 · 39 · 11 · 13 |
Discriminant |
Eigenvalues |
2+ 3+ 2 0 11+ 13+ 6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5184,-143640] |
[a1,a2,a3,a4,a6] |
Generators |
[390:7560:1] |
Generators of the group modulo torsion |
j |
764411904/143 |
j-invariant |
L |
8.3865418561925 |
L(r)(E,1)/r! |
Ω |
0.56264981666886 |
Real period |
R |
3.7263594548423 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
3.9999999998833 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368da1 5148b1 82368j1 |
Quadratic twists by: -4 8 -3 |