1919.sagews

E1=EllipticCurve([-3,3]); E1.plot(-3,3)

E1=EllipticCurve([-6,5]); E1.plot(-3,3)

E=EllipticCurve([-15,18]); P=[7,16]; Q=[1,2]

E(P); E(Q)

E(P)+E(Q)

P+Q

2*E(P)

-E(P)

E(P)+ (-1)*E(P)

E.cremona_label()

E.conductor()

factor(_)

F=EllipticCurve(GF(13),[3,8])

F.abelian_group()

F([9,7])+F([1,8])

F([9,7])+F([9,7])

E=EllipticCurve('37a1')

E.gens()

[(0 : 0 : 1)]

P=E([0,0]); 20*P

(683916417/264517696 : -18784454671297/4302115807744 : 1)

E144169=E.change_ring(GF(144169))

E144169.abelian_group()

P=E144169([137945,99547])

Q= 1000*P; Q