Atkin-Lehner |
2- 3+ 7- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
68208bm |
Isogeny class |
Conductor |
68208 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-84519704199168 = -1 · 217 · 33 · 77 · 29 |
Discriminant |
Eigenvalues |
2- 3+ -2 7- -1 -1 -2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-7464,-504720] |
[a1,a2,a3,a4,a6] |
Generators |
[292:4704:1] |
Generators of the group modulo torsion |
j |
-95443993/175392 |
j-invariant |
L |
3.214118973327 |
L(r)(E,1)/r! |
Ω |
0.24206804118769 |
Real period |
R |
1.6597187703096 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000363 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8526j1 9744o1 |
Quadratic twists by: -4 -7 |