Atkin-Lehner |
3- 7+ 13- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
8463g |
Isogeny class |
Conductor |
8463 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
2304 |
Modular degree for the optimal curve |
Δ |
2970513 = 34 · 7 · 132 · 31 |
Discriminant |
Eigenvalues |
-1 3- 2 7+ 0 13- 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-767,8112] |
[a1,a2,a3,a4,a6] |
Generators |
[-32:28:1] |
Generators of the group modulo torsion |
j |
49905130150513/2970513 |
j-invariant |
L |
3.6579171704002 |
L(r)(E,1)/r! |
Ω |
2.4020978229947 |
Real period |
R |
3.0456021693903 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
25389d1 59241i1 110019x1 |
Quadratic twists by: -3 -7 13 |