Atkin-Lehner |
3+ 7+ 11+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
69531a |
Isogeny class |
Conductor |
69531 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
11712 |
Modular degree for the optimal curve |
Δ |
-3407019 = -1 · 3 · 74 · 11 · 43 |
Discriminant |
Eigenvalues |
0 3+ 2 7+ 11+ -6 -3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,33,41] |
[a1,a2,a3,a4,a6] |
Generators |
[-1:2:1] [26:101:8] |
Generators of the group modulo torsion |
j |
1605632/1419 |
j-invariant |
L |
8.0473032475527 |
L(r)(E,1)/r! |
Ω |
1.6328588205759 |
Real period |
R |
1.6427840435882 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999126 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69531k1 |
Quadratic twists by: -7 |