Atkin-Lehner |
2+ 3- 61- |
Signs for the Atkin-Lehner involutions |
Class |
8784c |
Isogeny class |
Conductor |
8784 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
3072 |
Modular degree for the optimal curve |
Δ |
-409826304 = -1 · 210 · 38 · 61 |
Discriminant |
Eigenvalues |
2+ 3- -1 -3 -3 -5 6 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3,-974] |
[a1,a2,a3,a4,a6] |
Generators |
[11:18:1] |
Generators of the group modulo torsion |
j |
-4/549 |
j-invariant |
L |
3.4102319722293 |
L(r)(E,1)/r! |
Ω |
0.76897235777853 |
Real period |
R |
1.1086978412596 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4392b1 35136bu1 2928d1 |
Quadratic twists by: -4 8 -3 |