Atkin-Lehner |
2- 31- 43- |
Signs for the Atkin-Lehner involutions |
Class |
85312bb |
Isogeny class |
Conductor |
85312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
121856 |
Modular degree for the optimal curve |
Δ |
-108526418944 = -1 · 210 · 31 · 434 |
Discriminant |
Eigenvalues |
2- -2 3 3 2 6 6 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1169,21703] |
[a1,a2,a3,a4,a6] |
j |
-172678690048/105982831 |
j-invariant |
L |
3.9120150325946 |
L(r)(E,1)/r! |
Ω |
0.97800375851894 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85312d1 21328c1 |
Quadratic twists by: -4 8 |