F := GF(83);
E := EllipticCurve([0, F ! 1]);
P := E ! [22,78];
R<x> := PolynomialRing(F);
f := x - P[1];
G := SubgroupScheme(E,f);
Order(P);
Points(G);

IsogenyFromKernel(G);

21
{@ (22 : 5 : 1), (22 : 78 : 1), (0 : 1 : 0) @}

IsogenyFromKernel(G: Subgroup scheme of C defined by x + 61)
IsogenyFromKernel(C: C,f: x + 61)
In file "/magma/package/Geometry/CrvEll/subgroup_schemes.m", line 9, column 29:
>>     return IsogenyFromKernel(C, f, 0 : Check:=Check);
                               ^
Runtime error in 'IsogenyFromKernel': Does not appear to be a kernel in Isogeny