Atkin-Lehner |
2- 3+ 7- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
68544dc |
Isogeny class |
Conductor |
68544 |
Conductor |
∏ cp |
40 |
Product of Tamagawa factors cp |
deg |
506880 |
Modular degree for the optimal curve |
Δ |
97899233596416 = 210 · 39 · 75 · 172 |
Discriminant |
Eigenvalues |
2- 3+ 2 7- -2 6 17+ -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-605664,181423800] |
[a1,a2,a3,a4,a6] |
Generators |
[342:3780:1] |
Generators of the group modulo torsion |
j |
1219067475001344/4857223 |
j-invariant |
L |
8.1899521317445 |
L(r)(E,1)/r! |
Ω |
0.52679073697782 |
Real period |
R |
1.5546879542608 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997416 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68544d1 17136t1 68544dh1 |
Quadratic twists by: -4 8 -3 |