Atkin-Lehner |
2+ 3+ 5+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
64320d |
Isogeny class |
Conductor |
64320 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
34816 |
Modular degree for the optimal curve |
Δ |
-3556638720 = -1 · 217 · 34 · 5 · 67 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ -1 -3 -2 -2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-321,-3519] |
[a1,a2,a3,a4,a6] |
Generators |
[24:45:1] [33:144:1] |
Generators of the group modulo torsion |
j |
-27995042/27135 |
j-invariant |
L |
7.664099295988 |
L(r)(E,1)/r! |
Ω |
0.54241233555055 |
Real period |
R |
1.7662069042472 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
64320cg1 8040k1 |
Quadratic twists by: -4 8 |