//
// code for finding the model y^2=f_22(x) for X_0(22) and the factorization of f_22 in Q[X]
//
_<x>:=PolynomialRing(Rationals());
C:=SimplifiedModel(SmallModularCurve(22));
C;
f:=x^6-4*x^4+20*x^3-40*x^2+48*x-32;
Factorization(f);





//
// code for finding the model y^2=f_23(x) for X_0(23) and the factorization of f_23 in Q[X]
//
_<x>:=PolynomialRing(Rationals());
C:=SimplifiedModel(SmallModularCurve(23));
C;
f:=x^6-8*x^5+2*x^4+2*x^3-11*x^2+10*x-7;
Factorization(f);





//
// code for finding the model y^2=f_26(x) for X_0(26) and the factorization of f_26 in Q[X]
//
_<x>:=PolynomialRing(Rationals());
C:=SimplifiedModel(SmallModularCurve(26));
C;
f:=x^6-8*x^5+8*x^4-18*x^3+8*x^2-8*x+1;
Factorization(f);





//
// code for finding the model y^2=f_28(x) for X_0(28) and the factorization of f_28 in Q[X]
//
_<x>:=PolynomialRing(Rationals());
C:=SimplifiedModel(SmallModularCurve(28));
C;
f:=4*x^6-12*x^5+25*x^4-30*x^3+25*x^2-12*x+4;
Factorization(f);					// this is the factorization of the normalized model, so we have to multiply it by 4, which is the leading coefficient of f





//
// code for finding the model y^2=f_29(x) for X_0(29) and the factorization of f_29 in Q[X]
//
_<x>:=PolynomialRing(Rationals());
C:=SimplifiedModel(SmallModularCurve(29));
C;
f:=x^6-4*x^5-12*x^4+2*x^3+8*x^2+8*x-7;
Factorization(f);





//
// code for finding the model y^2=f_30(x) for X_0(30) and the factorization of f_30 in Q[X]
//
_<x>:=PolynomialRing(Rationals());
C:=SimplifiedModel(SmallModularCurve(30));
C;
f:=x^8+14*x^7+79*x^6+242*x^5+441*x^4+484*x^3+316*x^2+112*x+16;
Factorization(f);





//
// code for finding the model y^2=f_31(x) for X_0(31) and the factorization of f_31 in Q[X]
//
_<x>:=PolynomialRing(Rationals());
C:=SimplifiedModel(SmallModularCurve(31));
C;
f:=x^6-8*x^5+6*x^4+18*x^3-11*x^2-14*x-3;
Factorization(f);





//
// code for finding the model y^2=f_33(x) for X_0(33) and the factorization of f_33 in Q[X]
//
_<x>:=PolynomialRing(Rationals());
C:=SimplifiedModel(SmallModularCurve(33));
C;
f:=x^8+10*x^6-8*x^5+47*x^4-40*x^3+82*x^2-44*x+33;
Factorization(f);





//
// code for finding the model y^2=f_35(x) for X_0(35) and the factorization of f_35 in Q[X]
//
_<x>:=PolynomialRing(Rationals());
C:=SimplifiedModel(SmallModularCurve(35));
C;
f:=x^8-4*x^7-6*x^6-4*x^5-9*x^4+4*x^3-6*x^2+4*x+1;
Factorization(f);





//
// code for finding the model y^2=f_39(x) for X_0(39) and the factorization of f_39 in Q[X]
//
_<x>:=PolynomialRing(Rationals());
C:=SimplifiedModel(SmallModularCurve(39));
C;
f:=x^8-6*x^7+3*x^6+12*x^5-23*x^4+12*x^3+3*x^2-6*x+1;
Factorization(f);





//
// code for finding the model y^2=f_40(x) for X_0(40) and the factorization of f_40 in Q[X]
//
_<x>:=PolynomialRing(Rationals());
C:=SimplifiedModel(SmallModularCurve(40));
C;
f:=x^8+8*x^6-2*x^4+8*x^2+1;
Factorization(f);





//
// code for finding the model y^2=f_41(x) for X_0(41) and the factorization of f_41 in Q[X]
//
_<x>:=PolynomialRing(Rationals());
C:=SimplifiedModel(SmallModularCurve(41));
C;
f:=x^8-4*x^7-8*x^6+10*x^5+20*x^4+8*x^3-15*x^2-20*x-8;
Factorization(f);





//
// code for finding the model y^2=f_46(x) for X_0(46) and the factorization of f_46 in Q[X]
//
_<x>:=PolynomialRing(Rationals());
C:=SimplifiedModel(SmallModularCurve(46));
C;
f:=x^12-2*x^11+5*x^10+6*x^9-26*x^8+84*x^7-113*x^6+134*x^5-64*x^4+26*x^3+12*x^2+8*x-7;
Factorization(f);





//
// code for finding the model y^2=f_47(x) for X_0(47) and the factorization of f_47 in Q[X]
//
_<x>:=PolynomialRing(Rationals());
C:=SimplifiedModel(SmallModularCurve(47));
C;
f:=x^10-6*x^9+11*x^8-24*x^7+19*x^6-16*x^5-13*x^4+30*x^3-38*x^2+28*x-11;
Factorization(f);





//
// code for finding the model y^2=f_48(x) for X_0(48) and the factorization of f_48 in Q[X]
//
_<x>:=PolynomialRing(Rationals());
C:=SimplifiedModel(SmallModularCurve(48));
C;
f:=x^8+14*x^4+1;
Factorization(f);





//
// code for finding the model y^2=f_50(x) for X_0(50) and the factorization of f_50 in Q[X]
//
_<x>:=PolynomialRing(Rationals());
C:=SimplifiedModel(SmallModularCurve(50));
C;
f:=x^6-4*x^5-10*x^3-4*x+1;
Factorization(f);





//
// code for finding the model y^2=f_59(x) for X_0(59) and the factorization of f_59 in Q[X]
//
_<x>:=PolynomialRing(Rationals());
C:=SimplifiedModel(SmallModularCurve(59));
C;
f:=x^12-8*x^11+22*x^10-28*x^9+3*x^8+40*x^7-62*x^6+40*x^5-3*x^4-24*x^3+20*x^2-4*x-8;
Factorization(f);





//
// code for finding the model y^2=f_71(x) for X_0(71) and the factorization of f_71 in Q[X]
//
_<x>:=PolynomialRing(Rationals());
C:=SimplifiedModel(SmallModularCurve(71));
C;
f:=x^14+4*x^13-2*x^12-38*x^11-77*x^10-26*x^9+111*x^8+148*x^7+x^6-122*x^5-70*x^4+30*x^3+40*x^2+4*x-11;
Factorization(f);