Atkin-Lehner |
3- 5- 17+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
68085j |
Isogeny class |
Conductor |
68085 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
93184 |
Modular degree for the optimal curve |
Δ |
-60305267475 = -1 · 313 · 52 · 17 · 89 |
Discriminant |
Eigenvalues |
2 3- 5- -1 5 -2 17+ 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-3567,-82845] |
[a1,a2,a3,a4,a6] |
Generators |
[1657170:27255995:5832] |
Generators of the group modulo torsion |
j |
-6885024845824/82723275 |
j-invariant |
L |
14.253995021337 |
L(r)(E,1)/r! |
Ω |
0.3086619206029 |
Real period |
R |
11.544989897693 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000481 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
22695f1 |
Quadratic twists by: -3 |