Atkin-Lehner |
2- 3+ 29+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
129456u |
Isogeny class |
Conductor |
129456 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
52992 |
Modular degree for the optimal curve |
Δ |
-4529924352 = -1 · 28 · 39 · 29 · 31 |
Discriminant |
Eigenvalues |
2- 3+ 0 2 3 -6 4 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-135,-3294] |
[a1,a2,a3,a4,a6] |
Generators |
[694:18280:1] |
Generators of the group modulo torsion |
j |
-54000/899 |
j-invariant |
L |
7.7558240479616 |
L(r)(E,1)/r! |
Ω |
0.59144712669353 |
Real period |
R |
6.5566503492412 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000036587 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
32364a1 129456ba1 |
Quadratic twists by: -4 -3 |