Atkin-Lehner |
3+ 13- 19- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
21489c |
Isogeny class |
Conductor |
21489 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
55680 |
Modular degree for the optimal curve |
Δ |
-37887236366499 = -1 · 33 · 135 · 194 · 29 |
Discriminant |
Eigenvalues |
0 3+ 3 -2 4 13- 3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,8341,-44512] |
[a1,a2,a3,a4,a6] |
Generators |
[64:864:1] |
Generators of the group modulo torsion |
j |
64169108728414208/37887236366499 |
j-invariant |
L |
4.6294919250238 |
L(r)(E,1)/r! |
Ω |
0.38024896743711 |
Real period |
R |
0.6087448384445 |
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 |
64467t1 |
Quadratic twists by: -3 |