TypeNo.41 

>	qc[41]:=x^4+y^4-y^2*z^2-x^3*z;

 

(1.1)

 

>	with(plots): with(algcurves): plot_real_curve(subs(z=1,qc[41]),x,y);

 

>	singularities(subs(z=1,qc[41]),x,y);

 

(1.2)

 

>	subs(z=t*x,qc[41]);

 

(1.3)

 

>	Q41:=mapfactor(subs({y=1,x=U},%),U);

 

(1.4)

 

>	subs(U=0,Q41); simplify(%);

 

(1.5)

 

(1.5)

 

>	Quartic_to_Weierstrass(Q41,[0,1]);

 

(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)

 

latex(y^2 = x^3-t^2*x^2+(-4+4*t)*x-4*t^2*(-1+t)); 

{y}^{2}={x}^{3}-{t}^{2}{x}^{2}+ \left( -4+4\,t \right) x-4\,{t}^{2}

 

\left( t-1 \right)

 

>

 

TypeNo.42 

>	qc[42]:=(z^2+x^2+6*x*y-4*y^2)^2-12*x*y*(x-y)*(x+4*y);

 

(2.1)

 

>	with(plots): with(algcurves): plot_real_curve(subs(z=1,qc[42]),x,y);

 

>	singularities(subs(z=1,qc[42]),x,y);

 

(2.2)

 

>	subs(y=t*x,qc[42]);

 

(2.3)

 

>	Q42:=mapfactor(subs({z=1,x=U},%),U);

 

(2.4)

 

>	subs(U=0,Q42); simplify(%);

 

(2.5)

 

(2.5)

 

>	Quartic_to_Weierstrass(Q42,[0,1]);

 

(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)

 

>

 

Type No. 43 

>	qc[43]:=x^4-y^3*z;

 

(3.1)

 

>	with(plots): with(algcurves): plot_real_curve(subs(z=1,qc[43]),x,y);

 

>	singularities(subs(z=1,qc[43]),x,y);

 

(3.2)

 

>	subs(y=t*(x-z),qc[43]);

 

(3.3)

 

>	Q43:=mapfactor(subs({z=1,x=U},%),U);

 

(3.4)

 

>	subs(U=1,Q43); simplify(%);

 

(3.5)

 

(3.5)

 

>	Quartic_to_Weierstrass(Q43,[1,1]);

 

(3.6)

 

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

 

(3.7)

 

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

 

(3.8)

 

>	Elliptic_surface(%);

 

(3.9)

 

(3.9)

 

>	Show_data();

 

(3.10)

 

(3.10)

 

(3.10)

 

(3.10)

 

(3.10)

 

(3.10)

 

(3.10)

 

(3.10)

 

(3.10)

 

(3.10)

 

>

 

TypeNo.44 

>	qc[44]:=(x^2-y*z)*(x^2+y*z);

 

(4.1)

 

>	with(plots): with(algcurves): plot_real_curve(subs(z=1,qc[44]),x,y);

 

>	singularities(subs(z=1,qc[44]),x,y);

 

(4.2)

 

>	subs(y=t*x+z,qc[44]);

 

(4.3)

 

>	Q44:=mapfactor(subs({z=1,x=U},%),U);

 

(4.4)

 

>	subs(U=0,Q44); simplify(%);

 

(4.5)

 

(4.5)

 

>	Quartic_to_Weierstrass(Q44,[0,I]);

 

(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.45 

>	qc[45]:=(y*z-x^2)^2-y^3*x;

 

(5.1)

 

>	with(plots): with(algcurves): plot_real_curve(subs(z=1,qc[45]),x,y);

 

>	singularities(subs(z=1,qc[45]),x,y);

 

(5.2)

 

>	subs(y=t*x+z,qc[45]);

 

(5.3)

 

>	Q45:=mapfactor(subs({z=1,x=U},%),U);

 

(5.4)

 

>	subs(U=0,Q45); simplify(%);

 

(5.5)

 

(5.5)

 

>	Quartic_to_Weierstrass(Q45,[0,1]);

 

(5.6)

 

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

 

(5.7)

 

>	mapfactor(subs({X=4*X,Y=8*Y},%[1]/64),[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.46 

>	qc[46]:=(y*z-x^2)^2-y^3*x;

 

(6.1)

 

>	with(plots): with(algcurves): plot_real_curve(subs(z=1,qc[46]),x,y);

 

>	singularities(subs(z=1,qc[46]),x,y);

 

(6.2)

 

>	subs(y=t*(x-z),qc[46]);

 

(6.3)

 

>	Q46:=mapfactor(subs({z=1,x=U},%),U);

 

(6.4)

 

>	subs(U=1,Q46); simplify(%);

 

(6.5)

 

(6.5)

 

>	Quartic_to_Weierstrass(Q46,[1,1]);

 

(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.47 

>	qc[47]:=(y*z-x^2)^2-y^3*x;

 

(7.1)

 

>	with(plots): with(algcurves): plot_real_curve(subs(z=1,qc[47]),x,y);

 

>	singularities(subs(z=1,qc[47]),x,y);

 

(7.2)

 

>	subs(z=t*(x-y),qc[47]);

 

(7.3)

 

>	Q47:=mapfactor(subs({y=1,x=U},%),U);

 

(7.4)

 

>	subs(U=1,Q47); simplify(%);

 

(7.5)

 

(7.5)

 

>	Quartic_to_Weierstrass(Q47,[1,0]);

 

(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.48 

>	qc[48]:=x^4+y^4+x^3*y-x*y^2*z;

 

(8.1)

 

>	with(plots): with(algcurves): plot_real_curve(subs(z=1,qc[48]),x,y);

 

>	singularities(subs(z=1,qc[48]),x,y);

 

(8.2)

 

>	subs(y=t*x-z,qc[48]);

 

(8.3)

 

>	Q48:=mapfactor(subs({z=1,x=U},%),U);

 

(8.4)

 

>	subs(U=0,Q48); simplify(%);

 

(8.5)

 

(8.5)

 

>	Quartic_to_Weierstrass(Q48,[0,1]);

 

(8.6)

 

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

 

(8.7)

 

>	mapfactor(subs({X=4*X,Y=8*Y},%[1]/64),[X,Y]);

 

(8.8)

 

>	Elliptic_surface(%);

 

(8.9)

 

(8.9)

 

>	Show_data();

 

(8.10)

 

(8.10)

 

(8.10)

 

(8.10)

 

(8.10)

 

(8.10)

 

(8.10)

 

(8.10)

 

(8.10)

 

(8.10)

 

>

 

TypeNo.49 

>	qc[49]:=x^4+y^4-x*y^2*z;

 

(9.1)

 

>	with(plots): with(algcurves): plot_real_curve(subs(z=1,qc[50]),x,y);

 

>	singularities(subs(z=1,qc[49]),x,y);

 

(9.2)

 

>	subs(z=t*y+2*x,qc[49]);

 

(9.3)

 

>	Q49:=mapfactor(subs({x=1,y=U},%),U);

 

(9.4)

 

>	subs(U=0,Q49); simplify(%);

 

(9.5)

 

(9.5)

 

>	Quartic_to_Weierstrass(Q49,[0,1]);

 

(9.6)

 

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

 

(9.7)

 

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

 

(9.8)

 

>	Elliptic_surface(%);

 

(9.9)

 

(9.9)

 

>	Show_data();

 

(9.10)

 

(9.10)

 

(9.10)

 

(9.10)

 

(9.10)

 

(9.10)

 

(9.10)

 

(9.10)

 

(9.10)

 

(9.10)

 

TypeNo.50 

>	qc[50]:=x^4+y^4-x*y^2*z;

 

(10.1)

 

>	with(plots): with(algcurves): plot_real_curve(subs(z=1,qc[50]),x,y);

 

>	singularities(subs(z=1,qc[50]),x,y);

 

(10.2)

 

>	subs(z=t*(y-x)+2*x,qc[50]);

 

(10.3)

 

>	Q50:=mapfactor(subs({x=1,y=U},%),U);

 

(10.4)

 

>	subs(U=1,Q50); simplify(%);

 

(10.5)

 

(10.5)

 

>	Quartic_to_Weierstrass(Q46,[1,0]);

 

(10.6)

 

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

 

(10.7)

 

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

 

(10.8)

 

>	Elliptic_surface(%);

 

(10.9)

 

(10.9)

 

>	Show_data();

 

(10.10)

 

(10.10)

 

(10.10)

 

(10.10)

 

(10.10)

 

(10.10)

 

(10.10)

 

(10.10)

 

(10.10)

 

(10.10)

 

>