Atkin-Lehner |
2+ 11+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
21472a |
Isogeny class |
Conductor |
21472 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
4992 |
Modular degree for the optimal curve |
Δ |
41569792 = 29 · 113 · 61 |
Discriminant |
Eigenvalues |
2+ -1 0 -2 11+ 5 5 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-528,4840] |
[a1,a2,a3,a4,a6] |
Generators |
[13:2:1] |
Generators of the group modulo torsion |
j |
31855013000/81191 |
j-invariant |
L |
3.8187236669567 |
L(r)(E,1)/r! |
Ω |
2.0413039632303 |
Real period |
R |
1.8707276014463 |
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 |
21472f1 42944j1 |
Quadratic twists by: -4 8 |