Atkin-Lehner |
2+ 3+ 7+ 11+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
8778b |
Isogeny class |
Conductor |
8778 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1920 |
Modular degree for the optimal curve |
Δ |
-1896048 = -1 · 24 · 34 · 7 · 11 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7+ 11+ 2 2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,19,-51] |
[a1,a2,a3,a4,a6] |
Generators |
[6:15:1] |
Generators of the group modulo torsion |
j |
697864103/1896048 |
j-invariant |
L |
2.1081057779118 |
L(r)(E,1)/r! |
Ω |
1.354220616386 |
Real period |
R |
1.5566930176692 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
70224cz1 26334bm1 61446bc1 96558ck1 |
Quadratic twists by: -4 -3 -7 -11 |