Atkin-Lehner |
2- 13- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
83824bg |
Isogeny class |
Conductor |
83824 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
471744 |
Modular degree for the optimal curve |
Δ |
-1346516912386048 = -1 · 212 · 139 · 31 |
Discriminant |
Eigenvalues |
2- -2 -4 2 -1 13- 2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,23435,1107939] |
[a1,a2,a3,a4,a6] |
Generators |
[9668:182351:64] |
Generators of the group modulo torsion |
j |
32768/31 |
j-invariant |
L |
2.8642090288022 |
L(r)(E,1)/r! |
Ω |
0.31581061163303 |
Real period |
R |
4.5346940990555 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999819126 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5239d1 83824bj1 |
Quadratic twists by: -4 13 |