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Results tagged with elliptic-curves
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user 56667
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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On discriminants of elliptic curves
Let $E/\mathbb{Q}$ be an elliptic curve over $\mathbb{Q}$ and $\Delta_E$ denote the discriminant of $E$. We say an elliptic curve has entanglement fields if the intersection of the $m_1$ and $m_2$ div …
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Finding $Q(\sqrt{-2})$-rational points on $X_0(33)$
P. Bruin and F. Najman have determined the exceptional quadratic points on $X_0(33)$.
See Table 8 of https://arxiv.org/pdf/1406.0655.pdf
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Elliptic curves with potential good reduction over a prescribed extension
Notation: Let $K/\mathbb{Q}$ be a quadratic number field; let $p\geq 3$ be a rational prime and let $\mathfrak{p}$ denote a prime lying above $p$; let $K_{\mathfrak{p}}$ denote the completion of $K$ w …
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