Atkin-Lehner |
2- 3+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
8214g |
Isogeny class |
Conductor |
8214 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
49248 |
Modular degree for the optimal curve |
Δ |
-656169134743296 = -1 · 28 · 33 · 377 |
Discriminant |
Eigenvalues |
2- 3+ -2 0 -4 -6 -6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,21191,-321529] |
[a1,a2,a3,a4,a6] |
j |
410172407/255744 |
j-invariant |
L |
0.58953552454029 |
L(r)(E,1)/r! |
Ω |
0.29476776227015 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
65712bb1 24642g1 222c1 |
Quadratic twists by: -4 -3 37 |