Atkin-Lehner |
2- 5- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
68450bi |
Isogeny class |
Conductor |
68450 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
1181952 |
Modular degree for the optimal curve |
Δ |
3110727749894144000 = 218 · 53 · 377 |
Discriminant |
Eigenvalues |
2- 0 5- 2 0 2 -6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-1173490,-481582863] |
[a1,a2,a3,a4,a6] |
Generators |
[-687:431:1] |
Generators of the group modulo torsion |
j |
557238592989/9699328 |
j-invariant |
L |
10.572887829098 |
L(r)(E,1)/r! |
Ω |
0.14520727601352 |
Real period |
R |
4.0451324019133 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999995964 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68450q1 1850f1 |
Quadratic twists by: 5 37 |