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Results tagged with elliptic-curves
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user 163830
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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Rational points on the elliptic curve $y^2 = x^{3} - t^{2}z^3$
Above equation shown below:
$y^2=x^3-t^2z^3$ ----(1)
Equation $(1)$ has parametric solution given below:
$x=m^4-3m^2+3$
$y=m(m^4-3m^2+3)^2$
$z=(m^2-1)(3m^2-m^4-3)$
$t=1$
For, $m=2$, we get:
$(x,y,z,t …
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