Atkin-Lehner |
3+ 7- 19+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
80997c |
Isogeny class |
Conductor |
80997 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
89088 |
Modular degree for the optimal curve |
Δ |
-257288833431 = -1 · 34 · 78 · 19 · 29 |
Discriminant |
Eigenvalues |
1 3+ -2 7- -2 -4 -4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-466,-24905] |
[a1,a2,a3,a4,a6] |
Generators |
[70:505:1] [1406:17819:8] |
Generators of the group modulo torsion |
j |
-95443993/2186919 |
j-invariant |
L |
8.8806513964541 |
L(r)(E,1)/r! |
Ω |
0.42527727644801 |
Real period |
R |
10.441013296636 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000172 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
11571h1 |
Quadratic twists by: -7 |