Atkin-Lehner |
2+ 3- 17+ 101- |
Signs for the Atkin-Lehner involutions |
Class |
82416c |
Isogeny class |
Conductor |
82416 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
1676160 |
Modular degree for the optimal curve |
Δ |
5960708613869303808 = 211 · 35 · 179 · 101 |
Discriminant |
Eigenvalues |
2+ 3- 0 -2 -4 -4 17+ -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1666728,-820402668] |
[a1,a2,a3,a4,a6] |
Generators |
[-684:306:1] |
Generators of the group modulo torsion |
j |
250027751026762663250/2910502252865871 |
j-invariant |
L |
5.6299966281937 |
L(r)(E,1)/r! |
Ω |
0.13296549058501 |
Real period |
R |
4.2341788086114 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000005465 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
41208a1 |
Quadratic twists by: -4 |