Atkin-Lehner |
3+ 5- 17- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
68085b |
Isogeny class |
Conductor |
68085 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
270336 |
Modular degree for the optimal curve |
Δ |
-11632960546875 = -1 · 39 · 58 · 17 · 89 |
Discriminant |
Eigenvalues |
-2 3+ 5- 5 -3 4 17- 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-567,164180] |
[a1,a2,a3,a4,a6] |
Generators |
[-42:337:1] |
Generators of the group modulo torsion |
j |
-1024192512/591015625 |
j-invariant |
L |
4.4564986216212 |
L(r)(E,1)/r! |
Ω |
0.57953115268625 |
Real period |
R |
0.48061465295716 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000903 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68085a1 |
Quadratic twists by: -3 |