Atkin-Lehner |
7+ 11+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
6853b |
Isogeny class |
Conductor |
6853 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
2240 |
Modular degree for the optimal curve |
Δ |
-63849401 = -1 · 72 · 114 · 89 |
Discriminant |
Eigenvalues |
1 1 -3 7+ 11+ -6 -3 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,95,145] |
[a1,a2,a3,a4,a6] |
Generators |
[-1:7:1] [23:109:1] |
Generators of the group modulo torsion |
j |
96260823287/63849401 |
j-invariant |
L |
6.0826723755282 |
L(r)(E,1)/r! |
Ω |
1.2319987997873 |
Real period |
R |
1.2343097202242 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
109648ba1 61677i1 47971e1 75383h1 |
Quadratic twists by: -4 -3 -7 -11 |