Atkin-Lehner |
3- 5+ 17- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
68085f |
Isogeny class |
Conductor |
68085 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
34816 |
Modular degree for the optimal curve |
Δ |
4218887025 = 38 · 52 · 172 · 89 |
Discriminant |
Eigenvalues |
1 3- 5+ -4 0 4 17- 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-405,400] |
[a1,a2,a3,a4,a6] |
Generators |
[-146:379:8] |
Generators of the group modulo torsion |
j |
10091699281/5787225 |
j-invariant |
L |
5.2549355329585 |
L(r)(E,1)/r! |
Ω |
1.1843055634321 |
Real period |
R |
2.2185725102278 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999990066 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
22695a1 |
Quadratic twists by: -3 |