Atkin-Lehner |
3+ 7- 11+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
82467b |
Isogeny class |
Conductor |
82467 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
10368000 |
Modular degree for the optimal curve |
Δ |
2.1500519772677E+22 |
Discriminant |
Eigenvalues |
-1 3+ -4 7- 11+ 2 17+ -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-36869447,-85869906650] |
[a1,a2,a3,a4,a6] |
j |
2393558463315519963/9284733153971 |
j-invariant |
L |
0.12256442284761 |
L(r)(E,1)/r! |
Ω |
0.061282183056608 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82467f1 1683b1 |
Quadratic twists by: -3 -7 |