Incoming links: Finitely generated group
The elliptic curve group of all elliptic curve over the rational numbers is always a finitely generated group.
The number of points may be either finite or infinite. But when infinite, it is still a finitely generated group.
For this reason, the rank of an elliptic curve over the rational numbers is always defined.
TODO example.
Number of elements of an elliptic curve over the rational numbers Updated 2024-12-15 +Created 1970-01-01
Can be finite or infinite! TODO examples. But it is always a finitely generated group.