507.sagews

for i in [1,2,3]:
    EllipticCurve([0,0,0,0,i]).torsion_subgroup();

Torsion Subgroup isomorphic to Multiplicative Abelian Group isomorphic to C6 associated to the Elliptic Curve defined by y^2 = x^3 + 1 over Rational Field Torsion Subgroup isomorphic to Trivial Abelian Group associated to the Elliptic Curve defined by y^2 = x^3 + 2 over Rational Field Torsion Subgroup isomorphic to Trivial Abelian Group associated to the Elliptic Curve defined by y^2 = x^3 + 3 over Rational Field

F.<z> = CyclotomicField(20);
b = (1/25)*(-4*z^5 - 3);
E = EllipticCurve([1-((1/4)*(5*b - 1)),-b,-b,0,0]);
E

Elliptic Curve defined by y^2 + (1/5*z^5+7/5)*x*y + (4/25*z^5+3/25)*y = x^3 + (4/25*z^5+3/25)*x^2 over Cyclotomic Field of order 20 and degree 8

E.torsion_subgroup()

Torsion Subgroup isomorphic to Multiplicative Abelian Group isomorphic to C10 x C5 associated to the Elliptic Curve defined by y^2 + (1/5*z^5+7/5)*x*y + (4/25*z^5+3/25)*y = x^3 + (4/25*z^5+3/25)*x^2 over Cyclotomic Field of order 20 and degree 8