Atkin-Lehner |
2- 3- 13+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
84162x |
Isogeny class |
Conductor |
84162 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
419328 |
Modular degree for the optimal curve |
Δ |
-12999484769856 = -1 · 26 · 3 · 138 · 83 |
Discriminant |
Eigenvalues |
2- 3- -3 2 -5 13+ 6 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-20537,-1147719] |
[a1,a2,a3,a4,a6] |
Generators |
[4512:6025:27] |
Generators of the group modulo torsion |
j |
-198461344537/2693184 |
j-invariant |
L |
10.942542479511 |
L(r)(E,1)/r! |
Ω |
0.1992436944926 |
Real period |
R |
4.5766996134716 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004259 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6474j1 |
Quadratic twists by: 13 |