Atkin-Lehner |
2- 3+ 5+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
64320bx |
Isogeny class |
Conductor |
64320 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
67584 |
Modular degree for the optimal curve |
Δ |
-1221075000000 = -1 · 26 · 36 · 58 · 67 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -2 0 4 -3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,1709,-46259] |
[a1,a2,a3,a4,a6] |
Generators |
[2404:16875:64] |
Generators of the group modulo torsion |
j |
8620168984064/19079296875 |
j-invariant |
L |
3.8230261036282 |
L(r)(E,1)/r! |
Ω |
0.4482082374878 |
Real period |
R |
2.1323939318932 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000665 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
64320ch1 32160j1 |
Quadratic twists by: -4 8 |