Atkin-Lehner |
2- 3+ 7+ 11- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
85008bh |
Isogeny class |
Conductor |
85008 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
248832 |
Modular degree for the optimal curve |
Δ |
-9117601726464 = -1 · 215 · 33 · 7 · 112 · 233 |
Discriminant |
Eigenvalues |
2- 3+ 3 7+ 11- -1 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-37224,-2755728] |
[a1,a2,a3,a4,a6] |
Generators |
[1398098:33381106:2197] |
Generators of the group modulo torsion |
j |
-1392658229178217/2225976984 |
j-invariant |
L |
6.7735262006716 |
L(r)(E,1)/r! |
Ω |
0.17183879527209 |
Real period |
R |
9.854477551535 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999980882 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10626f1 |
Quadratic twists by: -4 |