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Results tagged with nt.number-theory
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user 21956
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
4
votes
1
answer
1k
views
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
1
vote
1
answer
130
views
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?
- 345
14
votes
1
answer
1k
views
Elliptic curves and connected components
Are there elliptic curves of positive rank with two real connected components
in which all the rational points lie only on one component?
Concrete examples are really appreciated.
- 345