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How do I obtain the generator of a ellittic curve?Is E.gens() only for the generator for the free part of the group or is for torsion also?

sage: E=EllipticCurve([0,-1,0,-4,-2]) sage: E.gens() [(3 : 2 : 1)] sage: T=E.torsion_subgroup() sage: T.points() [(0 : 1 : 0), (-1 : 0 : 1)] What is the generator of the group E(Q)?Is it the point (3,2) only? or the point (3,2)+(-1,0)?

How do I obtain the generator of a ellittic curve?Is E.gens() only for the generator for the free part of the group or is for torsion also?

sage: E=EllipticCurve([0,-1,0,-4,-2]) sage: E.gens() [(3 : 2 : 1)] sage: T=E.torsion_subgroup() sage: T.points() [(0 : 1 : 0), (-1 : 0 : 1)] What is the generator of the group E(Q)?Is it the point (3,2) only? or the point (3,2)+(-1,0)?

How do I obtain the generator of a ellittic curve?Is E.gens() only for the generator for the free part of the group or is for torsion also?

sage: E=EllipticCurve([0,-1,0,-4,-2]) E=EllipticCurve([0,-1,0,-4,-2])

sage: E.gens() E.gens()

[(3 : 2 : 1)] 1)]

sage: T=E.torsion_subgroup() T=E.torsion_subgroup()

sage: T.points() T.points()

[(0 : 1 : 0), (-1 : 0 : 1)] 1)]

What is the generator of the group E(Q)?Is it the point (3,2) only? or the point (3,2)+(-1,0)?

 4 None FrédéricC 4385 ●3 ●37 ●93

How do I obtain the generator of a ellittic curve?Is E.gens() only for the generator for the free part of the group or is for torsion also?

sage: E=EllipticCurve([0,-1,0,-4,-2])

sage: E.gens()

[(3 : 2 : 1)]

sage: T=E.torsion_subgroup()

sage: T.points()

[(0 : 1 : 0), (-1 : 0 : 1)]

What is the generator of the group E(Q)?Is it the point (3,2) only? or the point (3,2)+(-1,0)?

 5 None FrédéricC 4385 ●3 ●37 ●93

How do I obtain the generator of a ellittic curve?Is elliptic curve? Is E.gens() only for the generator for the free part of the group or is for torsion also?

sage: E=EllipticCurve([0,-1,0,-4,-2])

E=EllipticCurve([0,-1,0,-4,-2]) sage: E.gens()

sage: E.gens()

[(3 : 2 : 1)]

1)] sage: T=E.torsion_subgroup()

T=E.torsion_subgroup() sage: T.points()

T.points() [(0 : 1 : 0), (-1 : 0 : 1)]

What is the generator of the group E(Q)?Is it the point (3,2) only? or the point (3,2)+(-1,0)?

 6 None FrédéricC 4385 ●3 ●37 ●93

How do I obtain the generator of a elliptic curve? Is E.gens() only for the generator for the free part of the group or is for torsion also?

Code:

sage:  E=EllipticCurve([0,-1,0,-4,-2])
sage: E.gens()   sage: E.gens()   [(3 : 2 : 1)]
sage: T=E.torsion_subgroup()
sage: T.points()
[(0 : 1 : 0), (-1 : 0 : 1)]1)]


What is the generator of the group E(Q)?Is it the point (3,2) only? or the point (3,2)+(-1,0)?

 7 None FrédéricC 4385 ●3 ●37 ●93

How do I obtain the generator of a elliptic curve? Is E.gens() only for the generator for the free part of the group or is for torsion also?

Code:

sage:  E=EllipticCurve([0,-1,0,-4,-2])
E = EllipticCurve([0,-1,0,-4,-2])
sage: E.gens()
[(3 : 2 : 1)]
sage: T=E.torsion_subgroup()
T = E.torsion_subgroup()
sage: T.points()
[(0 : 1 : 0), (-1 : 0 : 1)]


What is the generator of the group E(Q)?Is it the point (3,2) only? or the point (3,2)+(-1,0)?

 8 retagged FrédéricC 4385 ●3 ●37 ●93

How do I obtain the generator of a elliptic curve? Is E.gens() only for the generator for the free part of the group or is for torsion also?

Code:

sage: E = EllipticCurve([0,-1,0,-4,-2])
sage: E.gens()
[(3 : 2 : 1)]
sage: T = E.torsion_subgroup()
sage: T.points()
[(0 : 1 : 0), (-1 : 0 : 1)]


What is the generator of the group E(Q)?Is it the point (3,2) only? or the point (3,2)+(-1,0)?