Atkin-Lehner |
3+ 5+ 13- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
3315b |
Isogeny class |
Conductor |
3315 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
448 |
Modular degree for the optimal curve |
Δ |
89505 = 34 · 5 · 13 · 17 |
Discriminant |
Eigenvalues |
-1 3+ 5+ -4 -4 13- 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-26,38] |
[a1,a2,a3,a4,a6] |
Generators |
[-6:7:1] [-1:8:1] |
Generators of the group modulo torsion |
j |
1948441249/89505 |
j-invariant |
L |
2.2772855863689 |
L(r)(E,1)/r! |
Ω |
3.357977761014 |
Real period |
R |
1.3563434593338 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999996 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
53040co1 9945k1 16575h1 43095f1 |
Quadratic twists by: -4 -3 5 13 |