Atkin-Lehner |
2+ 5+ 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
32110b |
Isogeny class |
Conductor |
32110 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
54912 |
Modular degree for the optimal curve |
Δ |
309977673980 = 22 · 5 · 138 · 19 |
Discriminant |
Eigenvalues |
2+ 2 5+ -1 6 13+ -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-1693,-2127] |
[a1,a2,a3,a4,a6] |
Generators |
[-12:135:1] |
Generators of the group modulo torsion |
j |
658489/380 |
j-invariant |
L |
5.6458208978763 |
L(r)(E,1)/r! |
Ω |
0.81191504876379 |
Real period |
R |
3.4768544483026 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999997 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
32110bh1 |
Quadratic twists by: 13 |