> p := 2^94-3;
> F := FiniteField(p);
> X〈x&rang := PolynomialRing(F);
> Z〈z&rang := PolynomialRing(Integers());
> C := HyperellipticCurve(x^5+3*x^3+x^2+4*x+18996);
> J := Jacobian(C);
> a := -117945679626530;
> b := -3217880959839060804507909012;
> P := p^2*z^4 + a*p*z^3 + b*z^2 + a*z + 1;
> Factorization(Evaluate(P,1));

[ <2, 1>, <5, 1>, <11, 1>, <3566535076924229196226077384633029743859037115938187019, 1> ]

> j := Random(J);
> j;

(x^2 + 16085942347328348463961966400*x + 19153274058576995701056296801, 1949507817705086951367373464*x + 9792672498106497464485520072, 2)

> Evaluate(P,1)*j;

(1, 0, 0)

> 110*j;

(x^2 + 3280825725809392072010493191*x + 5521173494457376673049810882, 3465564458856388449359855940*x + 280089587400185233932022646, 2)

> C2 := QuadraticTwist(C);
> J2 := Jacobian(C2);
> j2 := Random(J2);
> j2;

(x^2 + 2066292290053453340823144751*x + 7317599116560290457803650713, 2373956818062756699925842366*x + 14392612030538679488662119226, 2)

> Evaluate(P,-1)*j2;

(1, 0, 0)


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