Atkin-Lehner |
2- 3- 7+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
72072bd |
Isogeny class |
Conductor |
72072 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
73728 |
Modular degree for the optimal curve |
Δ |
745934821632 = 28 · 37 · 7 · 114 · 13 |
Discriminant |
Eigenvalues |
2- 3- -2 7+ 11- 13- 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2271,2914] |
[a1,a2,a3,a4,a6] |
Generators |
[-1:72:1] |
Generators of the group modulo torsion |
j |
6940769488/3996993 |
j-invariant |
L |
5.579590423123 |
L(r)(E,1)/r! |
Ω |
0.76693859736585 |
Real period |
R |
1.8187865505669 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999984308 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
24024j1 |
Quadratic twists by: -3 |