Atkin-Lehner |
3+ 5- 17- 67- |
Signs for the Atkin-Lehner involutions |
Class |
17085c |
Isogeny class |
Conductor |
17085 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
2304 |
Modular degree for the optimal curve |
Δ |
-768825 = -1 · 33 · 52 · 17 · 67 |
Discriminant |
Eigenvalues |
-1 3+ 5- 0 -5 0 17- -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,0,42] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:6:1] [0:6:1] |
Generators of the group modulo torsion |
j |
-1/768825 |
j-invariant |
L |
4.2549271699632 |
L(r)(E,1)/r! |
Ω |
2.2549671491932 |
Real period |
R |
0.94345657573866 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51255d1 85425l1 |
Quadratic twists by: -3 5 |