Atkin-Lehner |
2- 3+ 13+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
84162k |
Isogeny class |
Conductor |
84162 |
Conductor |
∏ cp |
11 |
Product of Tamagawa factors cp |
deg |
3253536 |
Modular degree for the optimal curve |
Δ |
315520255834048512 = 211 · 313 · 132 · 833 |
Discriminant |
Eigenvalues |
2- 3+ -2 -1 4 13+ 2 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-6828299,-6870580423] |
[a1,a2,a3,a4,a6] |
j |
208340931315536616034633/1866983762331648 |
j-invariant |
L |
1.0273403218567 |
L(r)(E,1)/r! |
Ω |
0.093394576125133 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
84162b1 |
Quadratic twists by: 13 |