Atkin-Lehner |
5+ 7+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
77315b |
Isogeny class |
Conductor |
77315 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
541205 = 5 · 72 · 472 |
Discriminant |
Eigenvalues |
-1 -2 5+ 7+ -5 2 -4 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-46,111] |
[a1,a2,a3,a4,a6] |
Generators |
[5:1:1] [-2:15:1] |
Generators of the group modulo torsion |
j |
4879681/245 |
j-invariant |
L |
3.579750090059 |
L(r)(E,1)/r! |
Ω |
2.8856377174249 |
Real period |
R |
0.62027018645378 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000024 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
77315e1 |
Quadratic twists by: -47 |