Atkin-Lehner |
13+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
689a |
Isogeny class |
Conductor |
689 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
40 |
Modular degree for the optimal curve |
Δ |
689 = 13 · 53 |
Discriminant |
Eigenvalues |
-1 -2 -2 2 2 13+ -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-14,19] |
[a1,a2,a3,a4,a6] |
Generators |
[1:2:1] |
Generators of the group modulo torsion |
j |
304821217/689 |
j-invariant |
L |
1.033304817561 |
L(r)(E,1)/r! |
Ω |
5.104722329004 |
Real period |
R |
0.80968542534816 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
11024f1 44096j1 6201d1 17225e1 |
Quadratic twists by: -4 8 -3 5 |