Atkin-Lehner |
2+ 3+ 13+ 83- |
Signs for the Atkin-Lehner involutions |
Class |
84162c |
Isogeny class |
Conductor |
84162 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
940992 |
Modular degree for the optimal curve |
Δ |
-4991802151624704 = -1 · 213 · 32 · 138 · 83 |
Discriminant |
Eigenvalues |
2+ 3+ 2 5 0 13+ -7 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,24671,3064885] |
[a1,a2,a3,a4,a6] |
j |
2035680647/6119424 |
j-invariant |
L |
2.4349514935606 |
L(r)(E,1)/r! |
Ω |
0.30436893445191 |
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 |
84162l1 |
Quadratic twists by: 13 |