Atkin-Lehner |
2+ 3- 13- 29- |
Signs for the Atkin-Lehner involutions |
Class |
72384bm |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
98304 |
Modular degree for the optimal curve |
Δ |
73452966912 = 210 · 38 · 13 · 292 |
Discriminant |
Eigenvalues |
2+ 3- -2 2 2 13- -2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-14469,-674613] |
[a1,a2,a3,a4,a6] |
j |
327166871093248/71731413 |
j-invariant |
L |
3.4824358546774 |
L(r)(E,1)/r! |
Ω |
0.43530448141423 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72384cp1 4524a1 |
Quadratic twists by: -4 8 |