Atkin-Lehner |
2+ 3- 7- 13- 67- |
Signs for the Atkin-Lehner involutions |
Class |
36582d |
Isogeny class |
Conductor |
36582 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
269568 |
Modular degree for the optimal curve |
Δ |
81724689027072 = 212 · 36 · 7 · 13 · 673 |
Discriminant |
Eigenvalues |
2+ 3- 0 7- 0 13- 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-569621,165424736] |
[a1,a2,a3,a4,a6] |
Generators |
[-16699284:284854165:21952] |
Generators of the group modulo torsion |
j |
20439985897177861911625/81724689027072 |
j-invariant |
L |
5.3758755792442 |
L(r)(E,1)/r! |
Ω |
0.53483701956121 |
Real period |
R |
10.051427598739 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999983 |
(Analytic) order of Ш |
t |
6 |
Number of elements in the torsion subgroup |
Twists |
109746u1 |
Quadratic twists by: -3 |