Atkin-Lehner |
2+ 5+ 11+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
56870a |
Isogeny class |
Conductor |
56870 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
342144 |
Modular degree for the optimal curve |
Δ |
3546353327264000 = 28 · 53 · 119 · 47 |
Discriminant |
Eigenvalues |
2+ 0 5+ 0 11+ 4 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-155810,23537300] |
[a1,a2,a3,a4,a6] |
Generators |
[3812:232214:1] |
Generators of the group modulo torsion |
j |
177409591659/1504000 |
j-invariant |
L |
3.0635263607333 |
L(r)(E,1)/r! |
Ω |
0.44661023673285 |
Real period |
R |
6.8595077069151 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999995988 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
56870m1 |
Quadratic twists by: -11 |