Atkin-Lehner |
2+ 3+ 23- 41- |
Signs for the Atkin-Lehner involutions |
Class |
67896a |
Isogeny class |
Conductor |
67896 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
334080 |
Modular degree for the optimal curve |
Δ |
-183712412351232 = -1 · 28 · 39 · 232 · 413 |
Discriminant |
Eigenvalues |
2+ 3+ 0 -2 3 4 3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-232740,43221924] |
[a1,a2,a3,a4,a6] |
Generators |
[198:-2214:1] |
Generators of the group modulo torsion |
j |
-276697696896000/36459209 |
j-invariant |
L |
6.6186962090348 |
L(r)(E,1)/r! |
Ω |
0.54804702836889 |
Real period |
R |
0.25160159116711 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999987582 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
67896d1 |
Quadratic twists by: -3 |