This construction taks as input:and it produces an elliptic curve over a finite field of order $p$ as output.

- elliptic curve over the rational numbers
- a prime number $p$

The constructions is used in the Birch and Swinnerton-Dyer conjecture.

To do it, we just convert the coefficients $a$ and $b$ from the Equation "Definition of the elliptic curves" from rational numbers to elements of the finite field.

For example, suppose we have $a=3/4$ and we are using $p=11$.

For the denominator $4$, we just use the multiplicative inverse, e.g. supposing we have
where $4_{−1}=3mod11$ because $4×3=1mod11$, related: math.stackexchange.com/questions/1204034/elliptic-curve-reduction-modulo-p

$43 →3×4_{−1}mod11=3×3mod11=9mod11$

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