Atkin-Lehner |
2+ 3- 7+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
68544y |
Isogeny class |
Conductor |
68544 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
184320 |
Modular degree for the optimal curve |
Δ |
-44208998055936 = -1 · 221 · 311 · 7 · 17 |
Discriminant |
Eigenvalues |
2+ 3- 1 7+ 3 3 17+ -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-21612,1264048] |
[a1,a2,a3,a4,a6] |
j |
-5841725401/231336 |
j-invariant |
L |
2.5422835041026 |
L(r)(E,1)/r! |
Ω |
0.63557087361312 |
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 |
68544eh1 2142o1 22848ba1 |
Quadratic twists by: -4 8 -3 |