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An answer could be as follows: 'p=18446744073709551667' then define the field 'K.=GF(p^2)' over which we define the curve 'E = EllipticCurve(K,[1,0])'. Now use the code 'E.cardinality().factor()' to get the cardinality of $E$, which is $2^4 * 4999^2 * 922521708027083^2$. Use the code 'pts = E.gens()' to find the generators which turn out to be $((3967812587828368975a + 7437411822947458617 : 16672546567636985011a + 14299206839437184441 : 1)$,$ (8681109523785822829a + 7072963597633280041 : 15515941078240688329a + 11174851755365315891 : 1))$.

An answer could be as follows: 'p=18446744073709551667' then define the field 'K.=GF(p^2)' over which we define the curve 'E = EllipticCurve(K,[1,0])'. Now use the code 'E.cardinality().factor()' to get the cardinality of $E$, which is $2^4 * 4999^2 * 922521708027083^2$. Use the code 'pts = E.gens()' to find the generators which turn out to be $((3967812587828368975a + 7437411822947458617 : 16672546567636985011a + 14299206839437184441 : 1)$,$ (8681109523785822829a + 7072963597633280041 : 15515941078240688329a + 11174851755365315891 : 1))$.

An answer could be as follows: 'p=18446744073709551667' then define the field 'K.=GF(p^2)' 'K . < a >=GF(p^2)' over which we define the curve 'E = EllipticCurve(K,[1,0])'. Now use the code 'E.cardinality().factor()' to get the cardinality of $E$, which is $2^4 * 4999^2 * 922521708027083^2$. Use the code 'pts = E.gens()' to find the generators which turn out to be $((3967812587828368975a + 7437411822947458617 : 16672546567636985011a + 14299206839437184441 : 1)$,$ (8681109523785822829a + 7072963597633280041 : 15515941078240688329a + 11174851755365315891 : 1))$.

An answer could be as follows: 'p=18446744073709551667' then define the field 'K . < a >=GF(p^2)' over which we define the curve 'E = EllipticCurve(K,[1,0])'. Now use the code 'E.cardinality().factor()' to get the cardinality of $E$, which is $2^4 * 4999^2 * 922521708027083^2$. Use the code 'pts = E.gens()' to find the generators which turn out to be $((3967812587828368975${(3967812587828368975a + 7437411822947458617 : 16672546567636985011a + 14299206839437184441 : 1)$,$ 1), (8681109523785822829a + 7072963597633280041 : 15515941078240688329a + 11174851755365315891 : 1))$. 1)}$.

Let $P_1$ be the first point, that is 'P1=E(13308581970510900443a + 15361864644717267429, 12035351063104026383a + 6630581890190451124)' and use the code 'P1.order().factor()' to get the order of $P_1$, which is $2^2 * 4999 * 922521708027083$. Now, let 'Q1=2^2 * 922521708027083 * P1', then $Q_1$ is of the required order. We can repeat this with the other point.

An answer could be as follows: 'p=18446744073709551667' then define the field 'K . < a >=GF(p^2)' over which we define the curve 'E = EllipticCurve(K,[1,0])'. Now use the code 'E.cardinality().factor()' to get the cardinality of $E$, which is $2^4 * 4999^2 * 922521708027083^2$. Use the code 'pts = E.gens()' to find the generators which turn out to be ${(3967812587828368975a + 7437411822947458617 : 16672546567636985011a + 14299206839437184441 : 1), (8681109523785822829a + 7072963597633280041 : 15515941078240688329a + 11174851755365315891 : 1)}$.

Let $P_1$ be the first point, that is 'P1=E(13308581970510900443a + 15361864644717267429, 12035351063104026383a + 6630581890190451124)' and use the code 'P1.order().factor()' to get the order of $P_1$, which is $2^2 * 4999 * 922521708027083$. Now, let 'Q1=2^2 * 922521708027083 * P1', then $Q_1$ is of the required order. We can repeat this with the other point.