Atkin-Lehner |
2- 3+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
51984bq |
Isogeny class |
Conductor |
51984 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
414720 |
Modular degree for the optimal curve |
Δ |
288261364756267008 = 214 · 39 · 197 |
Discriminant |
Eigenvalues |
2- 3+ 2 0 -2 4 0 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-165699,-2592702] |
[a1,a2,a3,a4,a6] |
Generators |
[-17205:524502:125] |
Generators of the group modulo torsion |
j |
132651/76 |
j-invariant |
L |
7.1900364913819 |
L(r)(E,1)/r! |
Ω |
0.25666616094302 |
Real period |
R |
7.0032960957395 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000027 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6498d1 51984bs1 2736k1 |
Quadratic twists by: -4 -3 -19 |