Atkin-Lehner |
2- 3+ 11- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
68244b |
Isogeny class |
Conductor |
68244 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-55789120317744 = -1 · 24 · 34 · 117 · 472 |
Discriminant |
Eigenvalues |
2- 3+ 2 -2 11- 0 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-16617,904950] |
[a1,a2,a3,a4,a6] |
Generators |
[-106:1210:1] |
Generators of the group modulo torsion |
j |
-17903239168/1968219 |
j-invariant |
L |
5.6390364942056 |
L(r)(E,1)/r! |
Ω |
0.61138588467853 |
Real period |
R |
2.3058417913627 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000074 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6204a1 |
Quadratic twists by: -11 |