TypeNo.61 

>	qc[61]:=(x^2+y^2-x*z)^2-x^2*z^2-y^2*z^2;

 

(1.1)

 

>	with(plots): with(algcurves): plot_real_curve(subs(z=1,qc[61]),x,y);

 

Warning, the name changecoords has been redefined

 

>	singularities(subs(z=1,qc[61]),x,y);

 

(1.2)

 

>	subs(y=t*x+z,qc[61]);

 

(1.3)

 

>	Q61:=mapfactor(subs({z=1,x=U},%),U);

 

(1.4)

 

>	subs(U=0,Q61); simplify(%);

 

(1.5)

 

(1.5)

 

>	Quartic_to_Weierstrass(Q61,[0,0]);

 

(1.6)

 

>	step5(%[1],{x=X,z=Z,y=Y},{x,y,z});

 

(1.7)

 

>	mapfactor(subs({X=X,Y=Y},%[1]),[X,Y]);

 

(1.8)

 

>	Elliptic_surface(%);

 

(1.9)

 

(1.9)

 

>	Show_data();

 

(1.10)

 

(1.10)

 

(1.10)

 

(1.10)

 

(1.10)

 

(1.10)

 

(1.10)

 

(1.10)

 

(1.10)

 

(1.10)

 

TypeNo.62 

>	qc[62]:=(x^3-y^2*z)*y;

 

(2.1)

 

>	with(plots): with(algcurves): plot_real_curve(subs(z=1,qc[62]),x,y);

 

>	singularities(subs(z=1,qc[62]),x,y);

 

(2.2)

 

>	subs(y=t*(x-z),qc[62]);

 

(2.3)

 

>	Q62:=mapfactor(subs({z=1,x=U},%),U);

 

(2.4)

 

>	subs(U=1,Q62); simplify(%);

 

(2.5)

 

(2.5)

 

>	Quartic_to_Weierstrass(Q62,[1,0]);

 

(2.6)

 

>	step5(%[1],{x=X,z=Z,y=Y},{x,y,z});

 

(2.7)

 

>	mapfactor(subs({X=X,Y=Y},%[1]),[X,Y]);

 

(2.8)

 

>	Elliptic_surface(%);

 

(2.9)

 

(2.9)

 

>	Show_data();

 

(2.10)

 

(2.10)

 

(2.10)

 

(2.10)

 

(2.10)

 

(2.10)

 

(2.10)

 

(2.10)

 

(2.10)

 

(2.10)

 

TypeNo.63 

>	qc[63]:=(y*z-x^2)^2-y^3*x;

 

(3.1)

 

>	with(plots): with(algcurves): plot_real_curve(subs(z=1,qc[63]),x,y);

 

>	singularities(subs(z=1,qc[63]),x,y);

 

(3.2)

 

>	subs(z=t*x,qc[63]);

 

(3.3)

 

>	Q63:=mapfactor(subs({y=1,x=U},%),U);

 

(3.4)

 

>	subs(U=0,Q63); simplify(%);

 

(3.5)

 

(3.5)

 

>	Quartic_to_Weierstrass(Q63,[0,0]);

 

(3.6)

 

(3.7)

 

>	step5(%[1],{x=X,z=Z,y=Y},{x,y,z});

 

(3.8)

 

>	mapfactor(subs({X=X,Y=Y},%[1]),[X,Y]);

 

(3.9)

 

>	Elliptic_surface(%);

 

(3.10)

 

(3.10)

 

>	Show_data();

 

(3.11)

 

(3.11)

 

(3.11)

 

(3.11)

 

(3.11)

 

(3.11)

 

(3.11)

 

(3.11)

 

(3.11)

 

(3.11)

 

TypeNo.64 

>	qc[64]:=(x^2-y*z+y^2)*(x^2-y*z-y^2);

 

(4.1)

 

>	with(plots): with(algcurves): plot_real_curve(subs(z=1,qc[64]),x,y);

 

>	singularities(subs(z=1,qc[64]),x,y);

 

(4.2)

 

>	subs(y=t*(x-z),qc[64]);

 

(4.3)

 

>	Q64:=mapfactor(subs({z=1,x=U},%),U);

 

(4.4)

 

>	subs(U=1,Q64); simplify(%);

 

(4.5)

 

(4.5)

 

>	Quartic_to_Weierstrass(Q64,[1,1]);

 

(4.6)

 

>	step5(%[1],{x=X,z=Z,y=Y},{x,y,z});

 

(4.7)

 

>	mapfactor(subs({X=X,Y=Y},%[1]),[X,Y]);

 

(4.8)

 

>	Elliptic_surface(%);

 

(4.9)

 

(4.9)

 

>	Show_data();

 

(4.10)

 

(4.10)

 

(4.10)

 

(4.10)

 

(4.10)

 

(4.10)

 

(4.10)

 

(4.10)

 

(4.10)

 

(4.10)

 

TypeNo.65 

>	qc[65]:=x^4-y^3*z;

 

(5.1)

 

>	with(plots): with(algcurves): plot_real_curve(subs(z=1,qc[65]),x,y);

 

>	singularities(subs(z=1,qc[65]),x,y);

 

(5.2)

 

>	subs(z=t*y,qc[65]);

 

(5.3)

 

>	Q65:=mapfactor(subs({x=1,y=U},%),U);

 

(5.4)

 

>	subs(U=0,Q65); simplify(%);

 

(5.5)

 

(5.5)

 

>	Quartic_to_Weierstrass(Q65,[0,1]);

 

(5.6)

 

>	step5(%[1],{x=X,z=Z,y=Y},{x,y,z});

 

(5.7)

 

>	mapfactor(subs({X=X,Y=Y},%[1]),[X,Y]);

 

(5.8)

 

>	Elliptic_surface(%);

 

(5.9)

 

(5.9)

 

>	Show_data();

 

(5.10)

 

(5.10)

 

(5.10)

 

(5.10)

 

(5.10)

 

(5.10)

 

(5.10)

 

(5.10)

 

(5.10)

 

(5.10)

 

TypeNo.66 

>	qc[66]:=(x^2+y^2-x*z)^2-x^2*z^2-y^2*z^2;

 

(6.1)

 

>	with(plots): with(algcurves): plot_real_curve(subs(z=1,qc[66]),x,y);

 

>	singularities(subs(z=1,qc[66]),x,y);

 

(6.2)

 

>	subs(z=t*x,qc[66]);

 

(6.3)

 

>	Q66:=mapfactor(subs({y=1,x=U},%),U);

 

(6.4)

 

>	subs(U=0,Q66); simplify(%);

 

(6.5)

 

(6.5)

 

>	Quartic_to_Weierstrass(Q66,[0,1]);

 

(6.6)

 

>	step5(%[1],{x=X,z=Z,y=Y},{x,y,z});

 

(6.7)

 

>	mapfactor(subs({X=X,Y=Y},%[1]),[X,Y]);

 

(6.8)

 

>	Elliptic_surface(%);

 

(6.9)

 

(6.9)

 

>	Show_data();

 

(6.10)

 

(6.10)

 

(6.10)

 

(6.10)

 

(6.10)

 

(6.10)

 

(6.10)

 

(6.10)

 

(6.10)

 

(6.10)

 

TypeNo.67 

>	qc[67]:=(x^2-y*z)^2-x^3*y;

 

(7.1)

 

>	with(plots): with(algcurves): plot_real_curve(subs(z=1,qc[67]),x,y);

 

>	singularities(subs(z=1,qc[67]),x,y);

 

(7.2)

 

>	subs(y=t*(x+4*z)-16*z,qc[67]);

 

(7.3)

 

>	Q67:=mapfactor(subs({z=1,x=U},%),U);

 

(7.4)

 

>	subs(U=-4,Q67); simplify(%);

 

(7.5)

 

(7.5)

 

>	Quartic_to_Weierstrass(Q67,[-4,0]);

 

(7.6)

 

>	step5(%[1],{x=X,z=Z,y=Y},{x,y,z});

 

(7.7)

 

>	mapfactor(subs({X=X,Y=Y},%[1]),[X,Y]);

 

(7.8)

 

>	Elliptic_surface(%);

 

(7.9)

 

(7.9)

 

>	Show_data();

 

(7.10)

 

(7.10)

 

(7.10)

 

(7.10)

 

(7.10)

 

(7.10)

 

(7.10)

 

(7.10)

 

(7.10)

 

(7.10)

 

TypeNo.68 

>	qc[68]:=(x^2+3*y^2-x*z)^2-x^2*z^2-3*y^2*z^2;

 

(8.1)

 

>	with(plots): with(algcurves): plot_real_curve(subs(z=1,qc[68]),x,y);

 

>	singularities(subs(z=1,qc[68]),x,y);

 

(8.2)

 

>	subs(z=t*(x-y)-4*y,qc[68]);

 

(8.3)

 

>	Q68:=mapfactor(subs({y=1,x=U},%),U);

 

(8.4)

 

>	subs(U=1,Q68); simplify(%);

 

(8.5)

 

(8.5)

 

>	Quartic_to_Weierstrass(Q68,[1,0]);

 

(8.6)

 

(8.7)

 

>	step5(%[1],{x=X,z=Z,y=Y},{x,y,z});

 

(8.8)

 

>	mapfactor(subs({X=X,Y=Y},%[1]),[X,Y]);

 

(8.9)

 

>	Elliptic_surface(%);

 

(8.10)

 

(8.10)

 

>	Show_data();

 

(8.11)

 

(8.11)

 

(8.11)

 

(8.11)

 

(8.11)

 

(8.11)

 

(8.11)

 

(8.11)

 

(8.11)

 

(8.11)

 

TypeNo.69 

>	qc[69]:=x^4-y^3*z;

 

>

 

(9.1)

 

>	with(plots): with(algcurves): plot_real_curve(subs(z=1,qc[69]),x,y);

 

>	singularities(subs(z=1,qc[69]),x,y);

 

(9.2)

 

>	subs(z=t*x,qc[69]);

 

(9.3)

 

>	Q69:=mapfactor(subs({y=1,x=U},%),U);

 

(9.4)

 

>	subs(U=0,Q69); simplify(%);

 

(9.5)

 

(9.5)

 

>	Quartic_to_Weierstrass(Q69,[0,0]);

 

(9.6)

 

(9.7)

 

>	step5(%[1],{x=X,z=Z,y=Y},{x,y,z});

 

(9.8)

 

>	mapfactor(subs({X=X,Y=Y},%[1]),[X,Y]);

 

(9.9)

 

>	Elliptic_surface(%);

 

(9.10)

 

(9.10)

 

>	Show_data();

 

(9.11)

 

(9.11)

 

(9.11)

 

(9.11)

 

(9.11)

 

(9.11)

 

(9.11)

 

(9.11)

 

(9.11)

 

(9.11)

 

TypeNo.70 

>	qc[70]:=(x^2+y^2-z^2)*(y+z)*(y-z);

 

(10.1)

 

>	with(plots): with(algcurves): plot_real_curve(subs(z=1,qc[70]),x,y);

 

>	singularities(subs(z=1,qc[70]),x,y);

 

(10.2)

 

>	subs(y=t*x,qc[70]);

 

(10.3)

 

>	Q70:=mapfactor(subs({z=1,x=U},%),U);

 

(10.4)

 

>	subs(U=0,Q70); simplify(%);

 

(10.5)

 

(10.5)

 

>	Quartic_to_Weierstrass(Q70,[0,1]);

 

(10.6)

 

(10.7)

 

>	step5(%[1],{x=X,z=Z,y=Y},{x,y,z});

 

(10.8)

 

>	mapfactor(subs({X=X,Y=Y},%[1]),[X,Y]);

 

(10.9)

 

>	Elliptic_surface(%);

 

(10.10)

 

(10.10)

 

>	Show_data();

 

(10.11)

 

(10.11)

 

(10.11)

 

(10.11)

 

(10.11)

 

(10.11)

 

(10.11)

 

(10.11)

 

(10.11)

 

(10.11)

 

>