Atkin-Lehner |
2+ 31- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
23312a |
Isogeny class |
Conductor |
23312 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
26880 |
Modular degree for the optimal curve |
Δ |
2755727558656 = 211 · 315 · 47 |
Discriminant |
Eigenvalues |
2+ 1 -1 1 -4 -4 -4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-4136,-65452] |
[a1,a2,a3,a4,a6] |
Generators |
[-22:124:1] [2138:98836:1] |
Generators of the group modulo torsion |
j |
3821557067858/1345570097 |
j-invariant |
L |
8.2788193423252 |
L(r)(E,1)/r! |
Ω |
0.61256382044168 |
Real period |
R |
0.67575157608524 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999998 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11656a1 93248bh1 |
Quadratic twists by: -4 8 |