Atkin-Lehner |
2+ 3+ 7+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
68544f |
Isogeny class |
Conductor |
68544 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
184320 |
Modular degree for the optimal curve |
Δ |
-2519465570496 = -1 · 26 · 39 · 76 · 17 |
Discriminant |
Eigenvalues |
2+ 3+ -3 7+ -5 7 17+ 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-32994,2308014] |
[a1,a2,a3,a4,a6] |
Generators |
[85:343:1] |
Generators of the group modulo torsion |
j |
-3153242386944/2000033 |
j-invariant |
L |
4.0512054704224 |
L(r)(E,1)/r! |
Ω |
0.80455628520239 |
Real period |
R |
1.2588322112312 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000438 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68544r1 34272c1 68544l1 |
Quadratic twists by: -4 8 -3 |