[bbb120]

FindGroupOrder := function (p, sigma)
   K := GF(p);
   v := K ! (4*sigma);
   u := K ! (sigma^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;
p:=40122362455616221971122353;
sigma:=2334843726764251;
FindGroupOrder(p,sigma);

http://magma.maths.usyd.edu.au/calc/
magma calculator online

output
[ <2, 3>, <3, 1>, <5, 1>, <19, 1>, <71, 1>, <281, 1>, <331, 1>, <4271, 1>,
<8887, 1>, <70206001, 1> ]