Atkin-Lehner |
3- 5- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
12675bj |
Isogeny class |
Conductor |
12675 |
Conductor |
∏ cp |
27 |
Product of Tamagawa factors cp |
deg |
589680 |
Modular degree for the optimal curve |
Δ |
6271885852126171875 = 39 · 58 · 138 |
Discriminant |
Eigenvalues |
-1 3- 5- -4 5 13+ 2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-6962888,-7071390483] |
[a1,a2,a3,a4,a6] |
Generators |
[-1523:1774:1] |
Generators of the group modulo torsion |
j |
117161545345/19683 |
j-invariant |
L |
3.3287293529423 |
L(r)(E,1)/r! |
Ω |
0.092940837172586 |
Real period |
R |
1.3265027094845 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
38025ci1 12675d1 12675bh1 |
Quadratic twists by: -3 5 13 |