Atkin-Lehner |
7+ 37+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
85211b |
Isogeny class |
Conductor |
85211 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
394464 |
Modular degree for the optimal curve |
Δ |
-10024988939 = -1 · 78 · 37 · 47 |
Discriminant |
Eigenvalues |
1 3 3 7+ 0 -5 2 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-67678,6793667] |
[a1,a2,a3,a4,a6] |
j |
-5946830358777/1739 |
j-invariant |
L |
9.3076535262727 |
L(r)(E,1)/r! |
Ω |
1.0341837281031 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85211d1 |
Quadratic twists by: -7 |