Atkin-Lehner |
3+ 11- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
57717b |
Isogeny class |
Conductor |
57717 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
82368 |
Modular degree for the optimal curve |
Δ |
-306747558711 = -1 · 33 · 118 · 53 |
Discriminant |
Eigenvalues |
1 3+ -3 3 11- -2 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-10731,-426024] |
[a1,a2,a3,a4,a6] |
j |
-23613579/53 |
j-invariant |
L |
1.8760274857458 |
L(r)(E,1)/r! |
Ω |
0.23450343598817 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
57717h1 57717d1 |
Quadratic twists by: -3 -11 |