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Results tagged with elliptic-curves
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user 10670
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.
5
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1
answer
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The name of the equianharmonic curve
I have found several references where the elliptic curve $y^2=x^3-1$ is called the equianharmonic curve, and, more often, where the half-period of this curve
$$ \omega_1 = \frac{\Gamma(1/3)^3}{4\pi} $ …
- 854
16
votes
2
answers
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Congruence for the number of points in the elliptic curve $y^2 = x^3+b \pmod{p}$
Let $E$ be the elliptic curve $y^2=x^3+1$ and $p \equiv 1 \pmod{3}$ a prime. Computing the number of points mod $p$ of $E$ using the naive method gives:
$$ \#E(\mathbb F_p) = 1+ \sum_{x=0}^{p-1} \left …
- 854