Curves over Finite Fields

Plot an arbitrary curve under modular arithmetic (i.e. over \( \mathbb{F}_p\)).
Enter curve parameters and press 'Draw!'.

Note: Choose \(p\) prime (like ...,43,47,53,59,61,67,71,73,79,83,89,97,101,109,...), otherwise \( \mathbb{F}_p\) won't be a field!

Curve Parameters

Curve Plot for

Tips

Click/tap a point to view its coordinates.
No ideas? Try one of these (by clicking on it):
- \(y^2+y = 3*x^3 +2*x^2 + x + 1 \mod 53\)
- \(x^2 = y^2 \mod 109\) - a cross
- \(y^2 = x^3 + 2*x + 1 \mod 53\) - an elliptic curve
- \(x^2 + y^2 \lt 20 \mod 109\) - would be filled circle in \(\mathbb{R}\)
- \(x * y \lt 14 \mod 109\)
- \(y = 2^x \mod 47\)
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© Sascha Grau, 2017, 2018