Atkin-Lehner |
2+ 3+ 67+ |
Signs for the Atkin-Lehner involutions |
Class |
9648a |
Isogeny class |
Conductor |
9648 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
3840 |
Modular degree for the optimal curve |
Δ |
-1350411264 = -1 · 210 · 39 · 67 |
Discriminant |
Eigenvalues |
2+ 3+ 3 -1 -2 4 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,189,1458] |
[a1,a2,a3,a4,a6] |
Generators |
[27:162:1] |
Generators of the group modulo torsion |
j |
37044/67 |
j-invariant |
L |
5.3622946282583 |
L(r)(E,1)/r! |
Ω |
1.0461867636869 |
Real period |
R |
1.2813903822872 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4824a1 38592bo1 9648b1 |
Quadratic twists by: -4 8 -3 |