Atkin-Lehner |
2- 3- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
1098j |
Isogeny class |
Conductor |
1098 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
192 |
Modular degree for the optimal curve |
Δ |
-711504 = -1 · 24 · 36 · 61 |
Discriminant |
Eigenvalues |
2- 3- -1 -5 3 -3 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,22,-7] |
[a1,a2,a3,a4,a6] |
Generators |
[3:7:1] |
Generators of the group modulo torsion |
j |
1685159/976 |
j-invariant |
L |
3.1674557478253 |
L(r)(E,1)/r! |
Ω |
1.6996525301653 |
Real period |
R |
0.23294877126425 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8784q1 35136v1 122a1 27450r1 |
Quadratic twists by: -4 8 -3 5 |