Elliptic Curve.sagews

E=EllipticCurve(GF(11),[-5,4]);
Ord=E.points();
print E
print Ord
print E.cardinality();

Elliptic Curve defined by y^2 = x^3 + 6*x + 4 over Finite Field of size 11 [(0 : 1 : 0), (0 : 2 : 1), (0 : 9 : 1), (1 : 0 : 1), (3 : 4 : 1), (3 : 7 : 1), (4 : 2 : 1), (4 : 9 : 1), (5 : 4 : 1), (5 : 7 : 1), (6 : 5 : 1), (6 : 6 : 1), (7 : 2 : 1), (7 : 9 : 1), (8 : 5 : 1), (8 : 6 : 1)] 16

E.plot(pointsize=10);

E=EllipticCurve([2,5]);
Ep = plot(E,thickness=1);
//p1 = (0,1); p2 = (0,4); p3=(0,7); p4 = (3,4); p5 = (3,7);
//p6 = (4,0); p7 = (8,4); p8 = (8,7); p9 = (9,2); p10 = (9,9);
//T1 = text('P=(0,1)',[0.1,1.5]);
//P = point([p1,p2,p3,p4,p5,p6,p7,p8,p9,p10],pointsize=20);
//show(Ep+P+T1);
//print E
Ep.plot();

Traceback (most recent call last): //show(Ep+P+T1); File "", line 1, in <module> File "/tmp/tmpqOM5Mq/___code___.py", line 5 //p1 = (_sage_const_0 ,_sage_const_1 ); p2 = (_sage_const_0 ,_sage_const_4 ); p3=(_sage_const_0 ,_sage_const_7 ); p4 = (_sage_const_3 ,_sage_const_4 ); p5 = (_sage_const_3 ,_sage_const_7 ); ^ SyntaxError: invalid syntax

E = EllipticCurve(FiniteField(11),[2,5]);
P = plot(E,rgbcolor=(0,0,1));

show(P);

E = EllipticCurve(GF(11),[-5,4]);
Ep=E.plot(pointsize=30,figsize=[6,4]);
p1=(7,2);
P = point([p1],pointsize=20);
T1 = text('P=(3,4)',[2.5,4]);
T2 = text('Q=(4,9)',[3.5,9]);
T3 = text('-R=(7,9)',[6.5,9.5]);
T4 = text('R=(7,2)',[6.5,2]);
L1 = line([(2.4,1),(4.2,10)],rgbcolor=(1,0,0));
L2 = line([(4,9),(8,9)],rgbcolor=(1,0,0));
L3 = line([(7,1),(7,11)],rgbcolor=(0,1,0));
show(Ep+T1+T2+T3+T4+L1+L2+L3);

E = EllipticCurve(GF(11),[-5,4]);
P=E(3,4);
Q=E(4,9);
R=2*P;
print R;

(5 : 7 : 1)

E = EllipticCurve(GF(11),[-5,4]);
Ep=E.plot(pointsize=50,figsize=[6,4]);
p1=(3,4);
P = point([p1],pointsize=20,rgbcolor=(0,1,0));
T1 = text('P=(3,4)',[2.5,4]);
T2 = text('-R=(5,4)',[4.5,3.5]);
T3 = text('R=(5,7)',[4.5,6.4]);
L1 = line([(3,4),(6,4)],rgbcolor=(1,0,0));
L2 = line([(5,2),(5,8)],rgbcolor=(0,1,0));
show(Ep+P+T1+L1+L2+T2+T3);