Atkin-Lehner |
2+ 3- 7- 11- 37- |
Signs for the Atkin-Lehner involutions |
Class |
51282s |
Isogeny class |
Conductor |
51282 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
393216 |
Modular degree for the optimal curve |
Δ |
27712805252090112 = 28 · 37 · 74 · 11 · 374 |
Discriminant |
Eigenvalues |
2+ 3- -2 7- 11- 2 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-80568,3671104] |
[a1,a2,a3,a4,a6] |
Generators |
[288:1928:1] |
Generators of the group modulo torsion |
j |
79339044305791873/38014822019328 |
j-invariant |
L |
4.0145786886461 |
L(r)(E,1)/r! |
Ω |
0.33355452876699 |
Real period |
R |
0.37611716586287 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999698 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
17094u1 |
Quadratic twists by: -3 |