WOLFRAM|DEMONSTRATIONS PROJECT

Real Elliptic Curves

​
parameters of the plane
z = A x + B
A (rotation)
11
B (translation)
12
parameters of the surface
z =
2
x
-a
2
y
+b x
2
y
+ c
2
x
y
a
-1
b
0
c
0
The intersection of the surface
z=
3
x
-a
2
y
+bx
2
y
+c
2
x
y
with the plane
z=Ax+B
gives an elliptic curve or its degenerate form. The intersection curve is illustrated in real space.