Atkin-Lehner |
2- 3+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
2112u |
Isogeny class |
Conductor |
2112 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
768 |
Modular degree for the optimal curve |
Δ |
138412032 = 222 · 3 · 11 |
Discriminant |
Eigenvalues |
2- 3+ -2 4 11+ 6 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-129,33] |
[a1,a2,a3,a4,a6] |
j |
912673/528 |
j-invariant |
L |
1.5514344999618 |
L(r)(E,1)/r! |
Ω |
1.5514344999618 |
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 |
2112r1 528j1 6336ci1 52800gp1 |
Quadratic twists by: -4 8 -3 5 |