show · ec.q all knowls · up · search:

An elliptic curve $E$ over $\mathbb{Q}$ has a Weierstrass equation of the form $$E : y^2 = x^3 + ax + b$$ with $a, b \in \mathbb{Z}$ such that its discriminant $$\Delta := −16(4a^3 + 27b^2 ) \not = 0.$$ Note that such an equation is not unique and $E$ has a unique minimal Weierstrass equation.

Knowl status:
  • Review status: reviewed
  • Last edited by Michael Bennett on 2019-04-10 17:59:13
Referred to by:
History: (expand/hide all) Differences (show/hide)