Atkin-Lehner |
3- 13+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
45123i |
Isogeny class |
Conductor |
45123 |
Conductor |
∏ cp |
40 |
Product of Tamagawa factors cp |
deg |
120960 |
Modular degree for the optimal curve |
Δ |
329766109049637 = 310 · 137 · 89 |
Discriminant |
Eigenvalues |
0 3- -2 -1 2 13+ -7 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-29969,1785671] |
[a1,a2,a3,a4,a6] |
Generators |
[1514:13685:8] [-177:1255:1] |
Generators of the group modulo torsion |
j |
616729673728/68319693 |
j-invariant |
L |
8.2748547396977 |
L(r)(E,1)/r! |
Ω |
0.52459583922217 |
Real period |
R |
0.39434427996831 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
3471d1 |
Quadratic twists by: 13 |