Atkin-Lehner |
5+ 37- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
82325b |
Isogeny class |
Conductor |
82325 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
54144 |
Modular degree for the optimal curve |
Δ |
-6431640625 = -1 · 59 · 37 · 89 |
Discriminant |
Eigenvalues |
1 0 5+ -2 -4 4 1 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-2042,36241] |
[a1,a2,a3,a4,a6] |
Generators |
[-58:1829:8] [24:-37:1] |
Generators of the group modulo torsion |
j |
-60282398961/411625 |
j-invariant |
L |
11.419727053618 |
L(r)(E,1)/r! |
Ω |
1.3444578639897 |
Real period |
R |
4.2469635380054 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000105 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16465b1 |
Quadratic twists by: 5 |