Atkin-Lehner |
2+ 3+ 5- 17+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
34170b |
Isogeny class |
Conductor |
34170 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
84480 |
Modular degree for the optimal curve |
Δ |
-20347221483630 = -1 · 2 · 34 · 5 · 174 · 673 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -3 3 2 17+ -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,168,-216954] |
[a1,a2,a3,a4,a6] |
Generators |
[1965:86151:1] |
Generators of the group modulo torsion |
j |
519524563319/20347221483630 |
j-invariant |
L |
3.2758204350232 |
L(r)(E,1)/r! |
Ω |
0.31477936335784 |
Real period |
R |
0.8672265975124 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999997 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
102510t1 |
Quadratic twists by: -3 |