Atkin-Lehner |
2- 3- 13+ 67+ |
Signs for the Atkin-Lehner involutions |
Class |
67938r |
Isogeny class |
Conductor |
67938 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
311040 |
Modular degree for the optimal curve |
Δ |
-101846519418384 = -1 · 24 · 39 · 136 · 67 |
Discriminant |
Eigenvalues |
2- 3- 3 1 0 13+ -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-24424,1545296] |
[a1,a2,a3,a4,a6] |
Generators |
[170:-1606:1] |
Generators of the group modulo torsion |
j |
-333822098953/21100176 |
j-invariant |
L |
15.375930715171 |
L(r)(E,1)/r! |
Ω |
0.58829218726431 |
Real period |
R |
0.36300769906007 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999996455 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
402d1 |
Quadratic twists by: 13 |