Atkin-Lehner |
2+ 3+ 7+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
69384a |
Isogeny class |
Conductor |
69384 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
297216 |
Modular degree for the optimal curve |
Δ |
-368108359363584 = -1 · 210 · 36 · 74 · 593 |
Discriminant |
Eigenvalues |
2+ 3+ -1 7+ 6 0 7 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,11744,778492] |
[a1,a2,a3,a4,a6] |
Generators |
[82:1512:1] |
Generators of the group modulo torsion |
j |
72852211964/149721291 |
j-invariant |
L |
5.6246951884777 |
L(r)(E,1)/r! |
Ω |
0.37129746650088 |
Real period |
R |
1.26239643759 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000915 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69384p1 |
Quadratic twists by: -7 |