Atkin-Lehner |
2+ 5+ 23- 37- |
Signs for the Atkin-Lehner involutions |
Class |
68080d |
Isogeny class |
Conductor |
68080 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
4800 |
Modular degree for the optimal curve |
Δ |
-68080 = -1 · 24 · 5 · 23 · 37 |
Discriminant |
Eigenvalues |
2+ 2 5+ 1 0 3 6 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,4,11] |
[a1,a2,a3,a4,a6] |
Generators |
[43:279:1] |
Generators of the group modulo torsion |
j |
340736/4255 |
j-invariant |
L |
9.7282400487206 |
L(r)(E,1)/r! |
Ω |
2.5674669257548 |
Real period |
R |
3.7890420130254 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999818 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34040e1 |
Quadratic twists by: -4 |