Atkin-Lehner |
2+ 5+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
650a |
Isogeny class |
Conductor |
650 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
192 |
Modular degree for the optimal curve |
Δ |
260000000 = 28 · 57 · 13 |
Discriminant |
Eigenvalues |
2+ 0 5+ 0 0 13+ -2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-167,-259] |
[a1,a2,a3,a4,a6] |
Generators |
[-11:18:1] |
Generators of the group modulo torsion |
j |
33076161/16640 |
j-invariant |
L |
1.615604580103 |
L(r)(E,1)/r! |
Ω |
1.3995225280679 |
Real period |
R |
1.1543969801854 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
5200n1 20800t1 5850bj1 130b1 |
Quadratic twists by: -4 8 -3 5 |