Atkin-Lehner |
2+ 3- 13+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
72384bg |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
497664 |
Modular degree for the optimal curve |
Δ |
1159977414915072 = 210 · 36 · 133 · 294 |
Discriminant |
Eigenvalues |
2+ 3- -4 -2 0 13+ 2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-33205,-1666021] |
[a1,a2,a3,a4,a6] |
Generators |
[-145:348:1] |
Generators of the group modulo torsion |
j |
3954096720707584/1132790444253 |
j-invariant |
L |
4.6057536044475 |
L(r)(E,1)/r! |
Ω |
0.36138822933403 |
Real period |
R |
1.0620511939574 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999980269 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72384cb1 4524c1 |
Quadratic twists by: -4 8 |