Atkin-Lehner |
11- 13- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
83369f |
Isogeny class |
Conductor |
83369 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
56000 |
Modular degree for the optimal curve |
Δ |
1220605529 = 116 · 13 · 53 |
Discriminant |
Eigenvalues |
1 -2 -2 -2 11- 13- 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-1697,-26985] |
[a1,a2,a3,a4,a6] |
Generators |
[1407:3703:27] |
Generators of the group modulo torsion |
j |
304821217/689 |
j-invariant |
L |
2.4282038505014 |
L(r)(E,1)/r! |
Ω |
0.74399281095053 |
Real period |
R |
6.5274927848077 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999908872 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
689a1 |
Quadratic twists by: -11 |