Atkin-Lehner |
3- 13- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
1209b |
Isogeny class |
Conductor |
1209 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
64 |
Modular degree for the optimal curve |
Δ |
-32643 = -1 · 34 · 13 · 31 |
Discriminant |
Eigenvalues |
0 3- 0 -2 1 13- -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-13,16] |
[a1,a2,a3,a4,a6] |
Generators |
[2:1:1] |
Generators of the group modulo torsion |
j |
-262144000/32643 |
j-invariant |
L |
2.5337776516054 |
L(r)(E,1)/r! |
Ω |
3.5843944209849 |
Real period |
R |
0.17672285426872 |
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 |
19344p1 77376a1 3627a1 30225a1 |
Quadratic twists by: -4 8 -3 5 |