Atkin-Lehner |
2+ 3+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
48672b |
Isogeny class |
Conductor |
48672 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
219648 |
Modular degree for the optimal curve |
Δ |
-90213291896832 = -1 · 212 · 33 · 138 |
Discriminant |
Eigenvalues |
2+ 3+ 2 3 -4 13+ -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-158184,24219728] |
[a1,a2,a3,a4,a6] |
Generators |
[169:1521:1] |
Generators of the group modulo torsion |
j |
-4852224 |
j-invariant |
L |
7.457537033428 |
L(r)(E,1)/r! |
Ω |
0.58655159705301 |
Real period |
R |
1.059517052845 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000019 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
48672bd1 97344r1 48672bf1 48672bg1 |
Quadratic twists by: -4 8 -3 13 |