Atkin-Lehner |
2- 3- 13+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
84162u |
Isogeny class |
Conductor |
84162 |
Conductor |
∏ cp |
243 |
Product of Tamagawa factors cp |
deg |
1516320 |
Modular degree for the optimal curve |
Δ |
682316956600201728 = 29 · 39 · 138 · 83 |
Discriminant |
Eigenvalues |
2- 3- 2 -3 -4 13+ 2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-453177,-110529927] |
[a1,a2,a3,a4,a6] |
Generators |
[-324:1683:1] |
Generators of the group modulo torsion |
j |
12617709776113/836448768 |
j-invariant |
L |
12.352026482175 |
L(r)(E,1)/r! |
Ω |
0.18477253715666 |
Real period |
R |
0.27510248805855 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000712 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
84162h1 |
Quadratic twists by: 13 |