sage: p = 137 sage: F = FiniteField(p) sage: E = EllipticCurve(F, [F.random_element(), F.random_element()]) sage: P = E.random_element() sage: print P (96 : 94 : 1) sage: time 102000823098320*P (86 : 60 : 1) CPU time: 0.12 s, Wall time: 0.13 s sage: show(plot(P) + plot(102000823098320*P,rgbcolor=(1,0,0))) [[a plot]]Now try with an elliptic curve over a huge field.
sage: p = next_prime(randrange(10^40)) sage: print p sage: F = FiniteField(p) sage: E = EllipticCurve(F, [F.random_element(), F.random_element()]) sage: P = E.random_element() sage: print P 554146695875703931136550843186162763121 (493257625218361211096484901389666856690 : 286863248034562484128552069228984577311 : 1)Then multiply...
sage: time 909238403284092384209482038402*P (151371634043111300277840422027192273952 : 333732213371771487412281506530764174375 : 1) CPU time: 0.20 s, Wall time: 0.21 s