Atkin-Lehner |
2+ 5+ 7+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
8470d |
Isogeny class |
Conductor |
8470 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
24192 |
Modular degree for the optimal curve |
Δ |
-2175952486400 = -1 · 221 · 52 · 73 · 112 |
Discriminant |
Eigenvalues |
2+ 1 5+ 7+ 11- 7 6 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-7934,280432] |
[a1,a2,a3,a4,a6] |
j |
-456390127585249/17983078400 |
j-invariant |
L |
1.6338568141782 |
L(r)(E,1)/r! |
Ω |
0.81692840708912 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
67760bq1 76230er1 42350cm1 59290bz1 |
Quadratic twists by: -4 -3 5 -7 |