Atkin-Lehner |
2- 3- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
2112z |
Isogeny class |
Conductor |
2112 |
Conductor |
∏ cp |
28 |
Product of Tamagawa factors cp |
deg |
5376 |
Modular degree for the optimal curve |
Δ |
1576599552 = 216 · 37 · 11 |
Discriminant |
Eigenvalues |
2- 3- -4 2 11+ 0 -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-32065,2199359] |
[a1,a2,a3,a4,a6] |
Generators |
[119:-288:1] |
Generators of the group modulo torsion |
j |
55635379958596/24057 |
j-invariant |
L |
3.0550931895174 |
L(r)(E,1)/r! |
Ω |
1.2243143160063 |
Real period |
R |
0.35647862522789 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
2112j1 528c1 6336cn1 52800ei1 |
Quadratic twists by: -4 8 -3 5 |