Atkin-Lehner |
2+ 3+ 7+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
63168f |
Isogeny class |
Conductor |
63168 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
11520 |
Modular degree for the optimal curve |
Δ |
-3095232 = -1 · 26 · 3 · 73 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ 4 7+ -3 -2 -3 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,9,-87] |
[a1,a2,a3,a4,a6] |
Generators |
[520:283:125] |
Generators of the group modulo torsion |
j |
1124864/48363 |
j-invariant |
L |
6.2948378161001 |
L(r)(E,1)/r! |
Ω |
1.2127046213488 |
Real period |
R |
5.1907428280504 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000461 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
63168bt1 31584y1 |
Quadratic twists by: -4 8 |