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Sage. I acme experiments with elliptic canes with segasagei I first define a fl•id mad 1028690:1 t Zaod(101)sage’ VRiug of integer. module 101sage. I ssamis at mnitip2ioatioa in Psage; sO)r(fl,Ssage: I define elliptic cern enr Psaga: C — flhipticcun.(140,IJ;sage, tEfliptic Cnne defined by r2 — r2 a Z over Ring *f integers module 101sage. P — r;randeepcint() -
sage: P(94 : 49 t 1)sager I not. coar4iaatas are La projective fern (S S : S.) representingsage: 4 pa2nt x — xlr, 7 — t!t, with s — 0 far point a infiatty.saga’ I get another paintsage: .Q —. *.raadom_paimt()eager p(2$ fl I 1):*mge tap(22 : 11 1)sagee I check coamutetivityflgi; QtP(21 77sages I get tUrd pointsager S — B,randam..point()seas, S(16 56 : 1)sage: * check asseciatiritysage: P a (Q+*)(SS : 2 •sage’ (P+9)+R(53 2 • I)sage, I find else of this groupsage. S.o.der(-)102saget I whst are factors at 502?sage, factar(i02)2k317saga: * so possible orders at elements are 1.2,3,I,17,S4,51102sages P.aèd.r(J$1 a.sage:. Q.order()Si:Saga; Lord.r()Sisager S nose of P,g, a are a generator (i.e. have Order 102)sage, I3et’. find onsaga. S — t.tndonjoint()
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O (0 a 1 1 0)1 (72 4 15 z 1)2 (2.5 a 80 a 1)1 (9 85 , 1)4 4*4 I 21 t 1)5 (52 s 44 . 1)4 (37 . 61 1.)7 (90 : 65 : 1)S (3$ 31. • 1)O (19 t 21. a10 (18 51. : 1)11 (92 : 14 1 1).12 (4 a 41 • 1)13 (38 1 38 a 1;14 (76 a 51 a 1.)nqe, I fled disent. lag of P. bias Its$ger R.dJSct,t.j.g(P)sonasa. 80R(96 I 49 : 1)saga: o0*anPflue,agei I tii4 ftscnte leg of g, base asage. a.ftecretajog(g)58509.: I dm4 elneats of each possible ordereage: a.order()
sage: S —sage. l.nrdar()51sage: S —
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