Atkin-Lehner |
2- 3+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
51984bk |
Isogeny class |
Conductor |
51984 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
656640 |
Modular degree for the optimal curve |
Δ |
-1923324112722198528 = -1 · 222 · 33 · 198 |
Discriminant |
Eigenvalues |
2- 3+ -2 -3 2 -1 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-61731,66984994] |
[a1,a2,a3,a4,a6] |
Generators |
[3249:-184832:1] [-241:8238:1] |
Generators of the group modulo torsion |
j |
-13851/1024 |
j-invariant |
L |
8.1002167433156 |
L(r)(E,1)/r! |
Ω |
0.2168798839384 |
Real period |
R |
1.5562025617251 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999997 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6498c1 51984bh1 51984bt1 |
Quadratic twists by: -4 -3 -19 |