> y := sqrt( (x&^3 + x + 4) mod 19);
Yielded these results:
> x :=0;
y := 2 --> y = +2 (mod 19) = 2 or 17 (mod 19)
> x :=1;
y := 6^1/2 --> no solution
> x:=2;
y := 141/2 --> no solution
> x :=3;
y := 15^1/2 --> no solution
> x :=4;
y := 15^1/2 --> no solution
> x :=5;
y := 1 --> y = +1 (mod 19) = 1 or 18 (mod 19)
> x :=6;
y := 17^1/2 --> no solution
> x :=7;
y := 23^1/2 --> no solution
> x :=8;
y := 11^1/2 --> no solution
> x :=9;
y := 1 --> y = +1 (mod 19) = 1 or 18 (mod 19)
> x :=10;
y := 7^1/2 --> no solution
> x :=11;
y := 4 --> y = +4(mod 19) = 4 or 15(mod 19)
> x :=12;
y := 15^1/2 --> no solution
> x :=13;
y := 10^1/2 --> no solution
> x :=14;
y := 7^1/2 --> no solution
> x :=15;
y := 23^1/2 --> no solution
> x :=16;
y := 2 31/2 --> no solution
> x :=17;
y := 13/2 --> no solution
> x :=18;
y := 21/2 --> no solution
> x :=19;
y := 2 --> y = +2 (mod 19) = 2 or 17 (mod 19)
x = Inf:
y = Inf
The points of this curve are:
(0, 2), (0, 17), (5, 1), (5, 18), (9, 1), (9, 18), (11, 4), (11, 15), (19, 2), (19, 17) and
(Inf, Inf)
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