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How many rational points does a random curve have? - MaRDI portal

How many rational points does a random curve have? (Q2864921)

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scientific article; zbMATH DE number 6233820

Language	Label	Description	Also known as
English	How many rational points does a random curve have?	scientific article; zbMATH DE number 6233820

Statements

scholarly article

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How many rational points does a random curve have? (English)

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publication date

27 November 2013

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zbMATH Keywords

rational points

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elliptic curve

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ranks

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describes a project that uses

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MaRDI profile type

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Average ranks of elliptic curves: Tension between data and conjecture

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Higher composition laws. II: On cubic analogues of Gauss composition

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Higher composition laws. III: The parametrization of quartic rings

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The density of discriminants of quartic rings and fields

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Higher composition laws. IV: The parametrization of quintic rings

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The density of discriminants of quintic rings and fields

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The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point

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Coregular spaces and genus one curves

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Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves

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Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0

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Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves

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Notes on elliptic curves. I.

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Notes on elliptic curves. II.

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On the modularity of elliptic curves over \(\mathbb Q\): wild 3-adic exercises

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The average rank of elliptic curves. I. (With an appendix by Oisín McGuinness: The explicit formula for elliptic curves over function fields)

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The behavior of the Mordell-Weil group of elliptic curves

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Class Groups of Number Fields: Numerical Heuristics

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Effective Chabauty

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Algorithmic Number Theory

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Efficient solution of rational conics

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Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves

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Density of discriminants of cubic extensions.

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On a Principle of Lipschitz

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On the Class-Number of Binary Cubic Forms (I)

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On a Principle of Lipschitz

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On the Density of Discriminants of Cubic Fields

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Heuristics on Tate-Shafarevitch Groups of Elliptic Curves Defined over Q

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Heuristics on class groups and on Tate-Shafarevich groups

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On the Birch-Swinnerton-Dyer quotients modulo squares

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Finiteness theorems for abelian varieties over number fields.

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Diophantine approximation on abelian varieties

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The size of Selmer groups for the congruent number problem

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The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky.

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The average analytic rank of elliptic curves

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Prehomogeneous vector spaces and field extensions. II

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The mean value of the product of class numbers of paired quadratic fields. I

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On the ranks of the 2-Selmer groups of twists of a given elliptic curve

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Random matrix theory and \(\zeta(1/2+it)\).

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Disparity in Selmer ranks of quadratic twists of elliptic curves

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Modular curves and the Eisenstein ideal

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Ranks of twists of elliptic curves and Hilbert's tenth problem

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Squarefree values of multivariable polynomials

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Bertini theorems over finite fields

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Average rank of elliptic curves

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Random maximal isotropic subspaces and Selmer groups

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Most odd degree hyperelliptic curves have only one rational point

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On zeta functions associated with prehomogeneous vector spaces

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The average measure of quadratic forms with given determinant and signature

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The distribution of ranks in families of quadratic twists of elliptic curves

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The Iwasawa Main Conjectures for \(\mathrm{GL}_{2}\)

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The effect of twisting on the 2-Selmer group

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A mean value theorem for the square of class number times regulator of quadratic extensions

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Secondary terms in counting functions for cubic fields

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Ring-theoretic properties of certain Hecke algebras

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Arithmetic invariant theory and 2-descent for plane quartic curves. With an appendix by Tasho Kaletha

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Siegel's theorem in the compact case

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Rank distribution in a family of cubic twists

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Some Heuristics about Elliptic Curves

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Modular elliptic curves and Fermat's Last Theorem

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Prehomogeneous vector spaces and field extensions

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Low-lying zeros of families of elliptic curves

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Average size of 2-Selmer groups of elliptic curves, II

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Average size of $2$-Selmer groups of elliptic curves, I

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Prehomogeneous vector spaces and field extensions. III

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Bulletin of the American Mathematical Society. New Series

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Identifiers

zbMATH Open document ID

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10.1090/S0273-0979-2013-01433-2

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2864921

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