Atkin-Lehner |
2+ 7+ 13+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
68614a |
Isogeny class |
Conductor |
68614 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
247296 |
Modular degree for the optimal curve |
Δ |
-76835308072432 = -1 · 24 · 7 · 138 · 292 |
Discriminant |
Eigenvalues |
2+ 2 2 7+ 4 13+ -4 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-2369,423077] |
[a1,a2,a3,a4,a6] |
Generators |
[-104117:1495606:2197] |
Generators of the group modulo torsion |
j |
-304821217/15918448 |
j-invariant |
L |
8.4164925619279 |
L(r)(E,1)/r! |
Ω |
0.50665056970079 |
Real period |
R |
8.3060131236522 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998177 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
5278f1 |
Quadratic twists by: 13 |