Atkin-Lehner |
3+ 5+ 11- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
50325f |
Isogeny class |
Conductor |
50325 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
184320 |
Modular degree for the optimal curve |
Δ |
-386932412109375 = -1 · 310 · 510 · 11 · 61 |
Discriminant |
Eigenvalues |
1 3+ 5+ 0 11- -2 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-50275,4420000] |
[a1,a2,a3,a4,a6] |
Generators |
[350:11975:8] [224:2000:1] |
Generators of the group modulo torsion |
j |
-899442534243889/24763674375 |
j-invariant |
L |
9.7883756337823 |
L(r)(E,1)/r! |
Ω |
0.53297013823296 |
Real period |
R |
9.182855596971 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
10065i1 |
Quadratic twists by: 5 |