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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 $y^2=x^3+2*x+3 \mod 53$

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 $\mathbb{R}$
- $x * y \lt 14 \mod 109$
- $y = 2^x \mod 49$
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© Sascha Grau, 2017, 2018