Atkin-Lehner |
3+ 13+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
45123f |
Isogeny class |
Conductor |
45123 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
169344 |
Modular degree for the optimal curve |
Δ |
4071186531477 = 36 · 137 · 89 |
Discriminant |
Eigenvalues |
-2 3+ 0 -1 0 13+ -3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-77458,8322810] |
[a1,a2,a3,a4,a6] |
Generators |
[256:2281:1] [175:310:1] |
Generators of the group modulo torsion |
j |
10648000000000/843453 |
j-invariant |
L |
4.1288743386493 |
L(r)(E,1)/r! |
Ω |
0.74473372094851 |
Real period |
R |
0.69301184814593 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
3471b1 |
Quadratic twists by: 13 |