Atkin-Lehner |
3- 7- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
6909i |
Isogeny class |
Conductor |
6909 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
3456 |
Modular degree for the optimal curve |
Δ |
-4031007687 = -1 · 36 · 76 · 47 |
Discriminant |
Eigenvalues |
-1 3- 0 7- 0 -6 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-393,4248] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:75:1] |
Generators of the group modulo torsion |
j |
-57066625/34263 |
j-invariant |
L |
3.0355853441174 |
L(r)(E,1)/r! |
Ω |
1.2877571163343 |
Real period |
R |
0.392877573161 |
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 |
110544cf1 20727o1 141b1 |
Quadratic twists by: -4 -3 -7 |