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// twist.cc: program to compute & display quadratic twists
//////////////////////////////////////////////////////////////////////////
//
// Copyright 1990-2012 John Cremona
//
// This file is part of the eclib package.
//
// eclib is free software; you can redistribute it and/or modify it
// under the terms of the GNU General Public License as published by the
// Free Software Foundation; either version 2 of the License, or (at your
// option) any later version.
//
// eclib is distributed in the hope that it will be useful, but WITHOUT
// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
// for more details.
//
// You should have received a copy of the GNU General Public License
// along with eclib; if not, write to the Free Software Foundation,
// Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA
//
//////////////////////////////////////////////////////////////////////////
#include <eclib/curve.h>
#include <eclib/getcurve.h>
int main(){
initprimes("PRIMES",0);
Curvedata D, E;
CurveRed CR;
bigint c4,c6,twist2;
bigint v;
int verbose=0;
vector<bigrational> ai(5);
while (getcurve(ai,verbose))
{
Curvedata D(Curvedata(ai,v),1);
E = D;
CR = CurveRed(E);
cout << "\nCurve is: " << endl; CR.display(cout);
long twist=1;
while(1)
{
cout << "\nEnter a twist value: ";
cout << "\n(0 to set a new `original' curve, 1 to twist original,\n";
cout << "or any other integer to twist immediately preceding output)\n ";
cin>>ws; if(cin.eof()) {cout<<endl; exit(0);}
cin >> twist;
if(twist==0) break;
if(twist==1) { E=D;}
else
{
E.getci(c4, c6);
twist *= 4; //corrects for twist not congruent -1 mod 4
twist2 = twist*twist;
c4 *= twist2;
c6 *= twist*twist2;
E = Curvedata(Curve(c4, c6), 1); //minimal form
CR=CurveRed(E);
cout << "\n\nE * " << twist/4 << " is: \n"; CR.display(cout);
cout << endl;
}
}
}
} //ends main
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