Atkin-Lehner |
2- 3+ 7+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
84084b |
Isogeny class |
Conductor |
84084 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
15552 |
Modular degree for the optimal curve |
Δ |
16480464 = 24 · 3 · 74 · 11 · 13 |
Discriminant |
Eigenvalues |
2- 3+ 1 7+ 11+ 13- 3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-65,78] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:14:1] |
Generators of the group modulo torsion |
j |
802816/429 |
j-invariant |
L |
5.5273335173362 |
L(r)(E,1)/r! |
Ω |
1.9240356840386 |
Real period |
R |
0.95759372884139 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003671 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
84084s1 |
Quadratic twists by: -7 |