Atkin-Lehner |
3+ 7- 13- 43- |
Signs for the Atkin-Lehner involutions |
Class |
82173d |
Isogeny class |
Conductor |
82173 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
2985984 |
Modular degree for the optimal curve |
Δ |
-2.4018526757294E+20 |
Discriminant |
Eigenvalues |
-1 3+ 2 7- 4 13- -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-968927,-831515644] |
[a1,a2,a3,a4,a6] |
Generators |
[1282:5306:1] [2348:98048:1] |
Generators of the group modulo torsion |
j |
-855083791508004577/2041541088941991 |
j-invariant |
L |
7.1973218084873 |
L(r)(E,1)/r! |
Ω |
0.071000759728304 |
Real period |
R |
11.263293889502 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999995925 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
11739g1 |
Quadratic twists by: -7 |