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Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.

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 …
Maleeha's user avatar
  • 83
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} …
Maleeha's user avatar
  • 83