Twists of elliptic curves
Mathematical curves that are isomorphic over algebraic closures / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Twists of elliptic curves?
Summarize this article for a 10 year old
SHOW ALL QUESTIONS
In the mathematical field of algebraic geometry, an elliptic curve E over a field K has an associated quadratic twist, that is another elliptic curve which is isomorphic to E over an algebraic closure of K. In particular, an isomorphism between elliptic curves is an isogeny of degree 1, that is an invertible isogeny. Some curves have higher order twists such as cubic and quartic twists. The curve and its twists have the same j-invariant.
Applications of twists include cryptography,[1] the solution of Diophantine equations,[2][3] and when generalized to hyperelliptic curves, the study of the Sato–Tate conjecture.[4]