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Results tagged with elliptic-curves
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user 21956
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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elliptic curves in form $y^2=x^3+p^2x$ where p is prime with rank 0
We Know that from a conjecture by Goldfeld says that half of all elliptic curves have rank zero.
Are there any known infinite families of elliptic curves in form
$y^2=x^3+p^2x$ where p is prime with …
- 345
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answer
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Integral points on a special curve
I tried to calculated the integral points for the following curve by Sage, but after a few hours I didn't receive any answer .
[0,0,0,-1609983754533564186692237854003906250000,0]
How can I calculate …
- 345
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Point of order 5 over an elliptic curve
For this curve $y^2=x^3+b^2x^2-a^2b^2x$ where $a \neq b$ and $a,b$ are rational. I can prove that if $b^2+4a^2$ is square then torsion group of curve is $\mathbb Z2 \times \mathbb Z2$,
and when $b^2+ …
- 345
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A special curve with points of order 3(or 6)
Could you please tell me what is the points of order 3 (or 6) Hon the elliptic curve $y^2=x^3+sx^2-x$ where
$$s = -\frac{1}{432}\frac{(81k^8-2592k^4-6912)}{k^6}$$ and $k$ is rational?
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