Atkin-Lehner |
2+ 3+ 13+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
72384f |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
1379283489792 = 210 · 36 · 133 · 292 |
Discriminant |
Eigenvalues |
2+ 3+ 0 2 -6 13+ 6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-3973,79429] |
[a1,a2,a3,a4,a6] |
Generators |
[-59:324:1] [-15:368:1] |
Generators of the group modulo torsion |
j |
6774679552000/1346956533 |
j-invariant |
L |
9.4278021756118 |
L(r)(E,1)/r! |
Ω |
0.8104124559837 |
Real period |
R |
5.8166690961279 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999329 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72384cw1 4524e1 |
Quadratic twists by: -4 8 |