Atkin-Lehner |
2- 3+ 13+ 83- |
Signs for the Atkin-Lehner involutions |
Class |
84162p |
Isogeny class |
Conductor |
84162 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
3015936 |
Modular degree for the optimal curve |
Δ |
-5380626865689811944 = -1 · 23 · 317 · 137 · 83 |
Discriminant |
Eigenvalues |
2- 3+ 3 -4 -3 13+ 2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-746054,-272292181] |
[a1,a2,a3,a4,a6] |
Generators |
[1076713717171:18276312563407:932574833] |
Generators of the group modulo torsion |
j |
-9514247050231273/1114737887016 |
j-invariant |
L |
8.7916046899774 |
L(r)(E,1)/r! |
Ω |
0.080691547640349 |
Real period |
R |
18.158871544519 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6474c1 |
Quadratic twists by: 13 |