Atkin-Lehner |
3- 7- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
6909j |
Isogeny class |
Conductor |
6909 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
3840 |
Modular degree for the optimal curve |
Δ |
348358689 = 32 · 77 · 47 |
Discriminant |
Eigenvalues |
-1 3- -2 7- 0 -2 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-3039,64224] |
[a1,a2,a3,a4,a6] |
Generators |
[57:249:1] |
Generators of the group modulo torsion |
j |
26383748833/2961 |
j-invariant |
L |
2.6061163608756 |
L(r)(E,1)/r! |
Ω |
1.637687562892 |
Real period |
R |
3.1826783324574 |
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 |
110544cp1 20727p1 987b1 |
Quadratic twists by: -4 -3 -7 |