Login
This is a place holder for potential sponsor logos.
examples of elliptic curves with complex multiplication
Here we show some elliptic curves defined over $\Rats$ which have complex multiplication by a quadratic imaginary field $K$ of class number $1$ (with $\operatorname{End}(E)$ exactly isomorphic to the full ring of integers $\mathcal{O}_K$ ).
| $K$ | Curve |
| $\Rats(\sqrt{-1})$ | $y^2=x^3+x$ |
| $\Rats(\sqrt{-2})$ | $y^2=x^3+4x^2+2x$ |
| $\Rats(\sqrt{-3})$ | $y^2+y=x^3$ |
| $\Rats(\sqrt{-7})$ | $y^2+xy=x^3-x^2-2x-1$ |
| $\Rats(\sqrt{-11})$ | $y^2+y=x^3-x^2-7x+10$ |
| $\Rats(\sqrt{-19})$ | $y^2+y=x^3-38x+90$ |
| $\Rats(\sqrt{-43})$ | $y^2+y=x^3-860x+9707$ |
| $\Rats(\sqrt{-67})$ | $y^2+y=x^3-7370x+243528$ |
| $\Rats(\sqrt{-163})$ | $y^2+y=x^3-2174420x+1234136692$ |
examples of elliptic curves with complex multiplication is owned by alozano.
None.