Álvaro Lozano‐Robledo

activity

20162024

most citedModels of CM elliptic curves with a prescribed

ℓ

-adic Galois image

2 citations · 2 across the 2 of their papers we have counts for

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5 papers · 1 filter

math.NT2024★ 2 cited

Models of CM elliptic curves with a prescribed $ℓ$ -adic Galois image

Enrique González-Jiménez, Álvaro Lozano-Robledo, Benjamin York

For each prime number $ℓ$ and for each imaginary quadratic order of class number one or two, we determine all the possible $ℓ$ -adic Galois representations that occur for any…

math.NT2023

Elliptic curves with complex multiplication and abelian division fields

Asimina S. Hamakiotes, Alvaro Lozano-Robledo

Let $K$ be an imaginary quadratic field, and let $O_{K, f}$ be an order in $K$ of conductor $f \geq 1$ . Let $E$ be an elliptic curve with CM by $O_{K, f}$ , such th…

math.NT2019

Rank and Bias in Families of Hyperelliptic Curves via Nagao's Conjecture

Trajan Hammonds, Seoyoung Kim, Benjamin Logsdon +2

Let $X : y^{2} = f (x)$ be a hyperelliptic curve over $Q (T)$ of genus $g \geq 1$ . Assume that the jacobian of $X$ over $Q (T)$ has no subvariety de…

math.NT2016

A probabilistic model for the distribution of ranks of elliptic curves over $Q$

Alvaro Lozano-Robledo

In this article, we propose a new probabilistic model for the distribution of ranks of elliptic curves in families of fixed Selmer rank, and compare the predictions with previous r…

math.NT2016

On the torsion of rational elliptic curves over quartic fields

Enrique Gonzalez-Jimenez, Alvaro Lozano-Robledo

Let E be an elliptic curve defined over Q and let G = E(Q)_tors be the associated torsion subgroup. We study, for a given G, which possible groups G <= H could appear such that H=E…