Atkin-Lehner |
3- 5- 7+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
12705m |
Isogeny class |
Conductor |
12705 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
115200 |
Modular degree for the optimal curve |
Δ |
-409478071153754295 = -1 · 36 · 5 · 78 · 117 |
Discriminant |
Eigenvalues |
1 3- 5- 7+ 11- 2 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,4232,30787601] |
[a1,a2,a3,a4,a6] |
j |
4733169839/231139696095 |
j-invariant |
L |
2.838718943897 |
L(r)(E,1)/r! |
Ω |
0.23655991199141 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
38115m1 63525r1 88935m1 1155m1 |
Quadratic twists by: -3 5 -7 -11 |