Atkin-Lehner |
3+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
249b |
Isogeny class |
Conductor |
249 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
8 |
Modular degree for the optimal curve |
Δ |
-249 = -1 · 3 · 83 |
Discriminant |
Eigenvalues |
1 3+ -1 -4 -3 2 4 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,2,1] |
[a1,a2,a3,a4,a6] |
Generators |
[0:1:1] |
Generators of the group modulo torsion |
j |
357911/249 |
j-invariant |
L |
1.5162589106946 |
L(r)(E,1)/r! |
Ω |
3.5061259800005 |
Real period |
R |
0.43245990570321 |
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 |
3984g1 15936l1 747e1 6225i1 |
Quadratic twists by: -4 8 -3 5 |