Atkin-Lehner |
2- 3+ 13- 29- |
Signs for the Atkin-Lehner involutions |
Class |
72384cp |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
8 |
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] |
Generators |
[-52:1133:1] [53:232:1] |
Generators of the group modulo torsion |
j |
327166871093248/71731413 |
j-invariant |
L |
7.2587763412375 |
L(r)(E,1)/r! |
Ω |
1.062275735291 |
Real period |
R |
3.4166159030477 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000005 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72384bm1 18096bb1 |
Quadratic twists by: -4 8 |