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Results tagged with elliptic-curves
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user 1018
An elliptic curve is an algebraic curve of genus one with some additional properties. Questions with this tag will often have the top-level tags nt.number-theory or ag.algebraic-geometry. Note also the tag arithmetic-geometry as well as some related tags such as rational-points, abelian-varieties, heights. Please do not use this tag for questions related to ellipses; instead use conic-sections.
75
votes
Accepted
Why is an elliptic curve a group?
Everything I am writing below is carried out explicitly in Chapter III of Silverman's book on elliptic curves. In the earlier chapters, he defines the Picard group.
For any curve over any field, algeb …
- 4,713
25
votes
Accepted
Definition and meaning of the conductor of an elliptic curve
The conductor of the curve and the conductor of the order in the endomorphism ring are not equal in the CM case; it's just unfortunate terminology. For example, y^2 = x^3 - x has complex multiplicatio …
- 4,713
6
votes
Elliptic Curves, Lattices, Lie Algebras
For a bit more info on question 3: if you are interested in the elliptic curve only as a complex Lie group, then when you identify it with C/L for C the complex plane and L a lattice, the Lie algebra …
- 4,713