Atkin-Lehner |
3+ 13+ 19+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
51129a |
Isogeny class |
Conductor |
51129 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
129600 |
Modular degree for the optimal curve |
Δ |
-3378233481363 = -1 · 33 · 133 · 195 · 23 |
Discriminant |
Eigenvalues |
1 3+ -4 -3 4 13+ 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-3144,-110681] |
[a1,a2,a3,a4,a6] |
Generators |
[718:4195:8] |
Generators of the group modulo torsion |
j |
-127316666284443/125119758569 |
j-invariant |
L |
3.4778299741777 |
L(r)(E,1)/r! |
Ω |
0.306567491092 |
Real period |
R |
5.6722093426471 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997983 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51129b1 |
Quadratic twists by: -3 |