Atkin-Lehner |
31- 59- |
Signs for the Atkin-Lehner involutions |
Class |
1829a |
Isogeny class |
Conductor |
1829 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
336 |
Modular degree for the optimal curve |
Δ |
-56699 = -1 · 312 · 59 |
Discriminant |
Eigenvalues |
-1 -3 3 -3 -2 -4 6 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,9,-6] |
[a1,a2,a3,a4,a6] |
Generators |
[6:12:1] |
Generators of the group modulo torsion |
j |
89314623/56699 |
j-invariant |
L |
1.2223910166682 |
L(r)(E,1)/r! |
Ω |
2.0247337871872 |
Real period |
R |
0.30186462645204 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
29264e1 117056g1 16461a1 45725b1 |
Quadratic twists by: -4 8 -3 5 |