Rank of an elliptic curve

Number of independent rational basis points with infinite order

In mathematics, the rank of an elliptic curve is the rational Mordell–Weil rank of an elliptic curve defined over the field of rational numbers or more generally a number field K. Mordell's theorem says the group of rational points on an elliptic curve has a finite basis. This means that for any elliptic curve there is a finite subset of the rational points on the curve, from which all further rational points may be generated. If the number of rational points on a curve is infinite then some point in a finite basis must have infinite order. The number of independent basis points with infinite order is the rank of the curve.

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