Atkin-Lehner |
2+ 3+ 7- 13- |
Signs for the Atkin-Lehner involutions |
Class |
1638d |
Isogeny class |
Conductor |
1638 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
288 |
Modular degree for the optimal curve |
Δ |
-830466 = -1 · 2 · 33 · 7 · 133 |
Discriminant |
Eigenvalues |
2+ 3+ -3 7- -3 13- 3 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-21,63] |
[a1,a2,a3,a4,a6] |
Generators |
[3:3:1] |
Generators of the group modulo torsion |
j |
-38958219/30758 |
j-invariant |
L |
1.8708802260666 |
L(r)(E,1)/r! |
Ω |
2.5885237692506 |
Real period |
R |
1.0841392968597 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
13104bi1 52416u1 1638n2 40950cx1 |
Quadratic twists by: -4 8 -3 5 |