Atkin-Lehner |
2- 3- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
48672bo |
Isogeny class |
Conductor |
48672 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
419328 |
Modular degree for the optimal curve |
Δ |
-411643250925244416 = -1 · 212 · 36 · 1310 |
Discriminant |
Eigenvalues |
2- 3- 1 0 4 13+ -3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-342732,83169632] |
[a1,a2,a3,a4,a6] |
Generators |
[-659:4779:1] |
Generators of the group modulo torsion |
j |
-10816 |
j-invariant |
L |
6.804321318528 |
L(r)(E,1)/r! |
Ω |
0.29220772844549 |
Real period |
R |
5.821476176154 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999912 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
48672n1 97344bi1 5408c1 48672p1 |
Quadratic twists by: -4 8 -3 13 |