Cover Image

Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Gajović, Stevan, Park, Sun Woo
Format:	Preprint
Published:	2025
Subjects:	Number Theory ! 11G05, 11G30, 14G05
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Cubic and quartic points on modular curves using generalised symmetric Chabauty
by: Box, Josha, et al.
Published: (2021)

Local-global principle for 11-isogenies of elliptic curves is true over quadratic fields
by: Gajović, Stevan, et al.
Published: (2025)

Infinitely many elliptic curves over $\mathbb{Q}(i)$ with rank 2 and $j$-invariant 1728
by: Savoie, Ben
Published: (2025)

Curves of genus two with maps of every degree to a fixed elliptic curve
by: Howe, Everett W.
Published: (2026)

Determining the rational points on a curve of genus 2 and Mordell-Weil rank 1
by: Stoll, Michael
Published: (2025)

Parity of ranks of Jacobians of curves
by: Dokchitser, Vladimir, et al.
Published: (2022)

A note on rank zero quadratic twists of a Mordell curve
by: Chutia, Ankurjyoti, et al.
Published: (2019)

Infinitely many cubic points on $X_0(N)/\langle w_d\rangle$ with $N$ square-free
by: Bars, Francesc, et al.
Published: (2024)

Examples of effectivity for integral points on certain curves of genus 2
by: Corvaja, Pietro, et al.
Published: (2024)

Rational points on modular curves via maps to elliptic curves with rank zero
by: Mayle, Jacob, et al.
Published: (2026)

Capitulation discriminants of genus one curves
by: Radicevic, Lazar
Published: (2022)

100% of elliptic curves with a marked point have positive rank
by: Park, Jun-Yong, et al.
Published: (2025)

Counting points on some genus zero Shimura curves
by: Genao, Tyler, et al.
Published: (2025)

Conductor exponents for families of hyperelliptic curves
by: Azon, Martin, et al.
Published: (2024)

Average analytic ranks of elliptic curves over number fields
by: Phillips, Tristan
Published: (2022)

A positive proportion of monic odd-degree hyperelliptic curves of genus $g \geq 4$ have no unexpected quadratic points
by: Laga, Jef, et al.
Published: (2024)

Rational and isolated quadratic points on hyperelliptic curves of rank 0 and small genus
by: Moussolo, Brice Miayoka
Published: (2025)

Some Obstructions to Solvable Points on Higher Genus Curves
by: Rawson, James
Published: (2022)

Selmer ranks in twists of CM abelian varieties
by: Shu, Jie
Published: (2025)

Shimura curve Atkin--Lehner quotients of genus at most two
by: Padurariu, Oana, et al.
Published: (2025)

Etale descent obstruction and anabelian geometry of curves over finite fields
by: Creutz, Brendan, et al.
Published: (2023)

Galois invariants of finite abelian descent and Brauer sets
by: Creutz, Brendan, et al.
Published: (2024)

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents
by: Keliher, Daniel, et al.
Published: (2025)

Counting rational points on elliptic and hyperelliptic curves over function fields
by: Gillibert, Jean, et al.
Published: (2025)

Unbounded average Selmer ranks of elliptic curves in torsion families
by: Phillips, Tristan
Published: (2025)

On the Selmer group and rank of a family of elliptic curves and curves of genus one violating the Hasse principle
by: Agathocleous, Eleni
Published: (2021)

On the infinitude of elliptic curves over a number field with prescribed small rank
by: Zywina, David
Published: (2026)

On the family of elliptic curves $y^2=x^3-m^2x + (pqr)^2$
by: Ghosh, Arkabrata
Published: (2024)

Linear and quadratic Chabauty for affine hyperbolic curves
by: Leonhardt, Marius, et al.
Published: (2023)

Rank of Jacobian Varieties of Curves $y^s=x(ax^r+b)$
by: Salami, Sajad
Published: (2025)

Cyclic Cubic Points on Higher Genus Curves
by: Rawson, James
Published: (2024)

Ranks of elliptic curves in cyclic sextic extensions of $\mathbb{Q}$
by: Kisilevsky, Hershy, et al.
Published: (2023)

Growth of points on hyperelliptic curves
by: Keyes, Christopher
Published: (2019)

Rank of the family of elliptic curves $y^2 = x^3- 5px$
by: Ghosh, Arkabrata
Published: (2025)

Sporadic points on $X_0(N)$
by: Derickx, Maarten, et al.
Published: (2025)

Non-simple abelian varieties in a family: arithmetic approaches
by: Fu, Yu
Published: (2024)

Analytic rank-one elliptic curves over function fields and their rank over certain ring class fields
by: Choi, Seokhyun, et al.
Published: (2026)

Affine Chabauty I
by: Leonhardt, Marius, et al.
Published: (2025)

Affine Chabauty II
by: Leonhardt, Marius, et al.
Published: (2026)

Prime order torsion on elliptic curves over number fields. Part I: Asymptotics
by: Derickx, Maarten, et al.
Published: (2025)