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Results tagged with arithmetic-geometry
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user 409515
Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
4
votes
1
answer
252
views
Finding the $K=\mathbb{Q}(\sqrt{6})$-rational points on the twist of $X_{0}(26)$
Let $K=\mathbb{Q}(\sqrt{6})$. I am looking to determine all $K$-rational points on the curve
$$C: y^{2}=3x^6-24x^5+24x^4-54x^3+24x^2-24x+3.$$
More precisely, $C$ is a twist of the modular curve $X_{0} …
- 83
2
votes
0
answers
54
views
Conductor of hyperelliptic curve after adding a rational root
Let $r\geq 5$ be a prime. Suppose I have a specified hyperelliptic curve $C: y^2=f(x)$ defined over $\mathbb{Q}$, where $f\in\mathbb{Q}[x]$ has degree $r$.
Note: the roots of $f$ are not rational but …
- 83