Atkin-Lehner |
2- 3+ 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
82764b |
Isogeny class |
Conductor |
82764 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
126720 |
Modular degree for the optimal curve |
Δ |
-2559211193088 = -1 · 28 · 33 · 117 · 19 |
Discriminant |
Eigenvalues |
2- 3+ -2 4 11- -1 -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,2904,-47916] |
[a1,a2,a3,a4,a6] |
Generators |
[45:417:1] |
Generators of the group modulo torsion |
j |
221184/209 |
j-invariant |
L |
6.8652807657165 |
L(r)(E,1)/r! |
Ω |
0.44380447148209 |
Real period |
R |
3.8672890897417 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000005173 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82764a1 7524b1 |
Quadratic twists by: -3 -11 |