Atkin-Lehner |
3+ 7- 13- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
49959a |
Isogeny class |
Conductor |
49959 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
11776 |
Modular degree for the optimal curve |
Δ |
-63997479 = -1 · 33 · 72 · 13 · 612 |
Discriminant |
Eigenvalues |
1 3+ 2 7- 0 13- -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-21,392] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:22:1] |
Generators of the group modulo torsion |
j |
-38958219/2370277 |
j-invariant |
L |
8.1768724901868 |
L(r)(E,1)/r! |
Ω |
1.6234646552305 |
Real period |
R |
2.5183401633875 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999668 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
49959b1 |
Quadratic twists by: -3 |