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Results tagged with elliptic-curves
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user 497795
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.
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Does this subset of elliptic curves over $\mathbb{Q}$ have positive proportion?
Let $E: y^2 = x^3 + Ax + B$ be a quasi-minimal elliptic curve over $\mathbb{Q}$, i.e. $\gcd(a^3, b^2)$ is $12$th power free. Furthermore, let $\operatorname{rank}(E) = 1$ and $j(E)=\frac{1728 \times 4 …
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Bounding $h_3(D)$ by number of points on an elliptic curve
According to Helfgott-Venkatesh, Let $E(D)$ denote the elliptic curve $y^2 = x^3 + D$, then $h_3(Q(\sqrt D))$, which is the 3-part of the class number of the Quadratic Field with discriminant $D$, or …
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Upper bound on number of integral solutions of elliptic curves
I was studying M. Bhargava Et al's seminal paper titled "Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves"
And came across a very fascinating observation tha …
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