Atkin-Lehner |
2+ 3- 29- 61- |
Signs for the Atkin-Lehner involutions |
Class |
31842p |
Isogeny class |
Conductor |
31842 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
84480 |
Modular degree for the optimal curve |
Δ |
-6351150806496 = -1 · 25 · 37 · 293 · 612 |
Discriminant |
Eigenvalues |
2+ 3- -3 -3 -2 -2 1 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-10746,448276] |
[a1,a2,a3,a4,a6] |
Generators |
[59:-160:1] [-81:925:1] |
Generators of the group modulo torsion |
j |
-188260594363297/8712141024 |
j-invariant |
L |
4.8427974922513 |
L(r)(E,1)/r! |
Ω |
0.74534211008726 |
Real period |
R |
0.27072565217084 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10614j1 |
Quadratic twists by: -3 |