Atkin-Lehner |
2+ 3+ 7+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
68208b |
Isogeny class |
Conductor |
68208 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
274176 |
Modular degree for the optimal curve |
Δ |
323937173581056 = 28 · 32 · 78 · 293 |
Discriminant |
Eigenvalues |
2+ 3+ -1 7+ 0 -5 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-85521,9615789] |
[a1,a2,a3,a4,a6] |
Generators |
[1146:-4263:8] [20:2813:1] |
Generators of the group modulo torsion |
j |
46873007104/219501 |
j-invariant |
L |
8.4313674336762 |
L(r)(E,1)/r! |
Ω |
0.54525644802154 |
Real period |
R |
0.85906237985548 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000042 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34104l1 68208z1 |
Quadratic twists by: -4 -7 |