Atkin-Lehner |
7+ 11- 89- |
Signs for the Atkin-Lehner involutions |
Class |
6853g |
Isogeny class |
Conductor |
6853 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
416 |
Modular degree for the optimal curve |
Δ |
-75383 = -1 · 7 · 112 · 89 |
Discriminant |
Eigenvalues |
-1 0 -2 7+ 11- -2 0 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,9,-10] |
[a1,a2,a3,a4,a6] |
Generators |
[5:9:1] |
Generators of the group modulo torsion |
j |
89314623/75383 |
j-invariant |
L |
1.7984410723448 |
L(r)(E,1)/r! |
Ω |
1.9022052761348 |
Real period |
R |
1.8909011502682 |
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 |
109648q1 61677c1 47971j1 75383g1 |
Quadratic twists by: -4 -3 -7 -11 |