Efficient solution of rational conics
From MaRDI portal
Publication:4806396
DOI10.1090/S0025-5718-02-01480-1zbMath1022.11031MaRDI QIDQ4806396
Publication date: 14 May 2003
Published in: Mathematics of Computation (Search for Journal in Brave)
efficient algorithmsDiophantine equationlattice basis reductionLegendre's equationrational conicshomogeneous quadratic polynomial with integer coefficients
Quadratic and bilinear Diophantine equations (11D09) [https://zbmath.org/classification/?q=cc:11G30 Curves of arbitrary genus or genus ( e 1) over global fields (11G30)]
Related Items
Improved torsion-point attacks on SIDH variants, Explicit equivalence of quadratic forms over \(\mathbb{F}_q(t)\), Computing with quadratic forms over number fields, Solving conics over functions fields, Uniformly counting rational points on conics, The anisotropic part of a quadratic form over a number field, Factorization and root-finding for polynomials over division quaternion algebras, Splitting quaternion algebras over quadratic number fields, Complete and computable orbit invariants in the geometry of the affine group over the integers, Hashing to elliptic curves through Cipolla-Lehmer-Müller's square root algorithm, On the number of solutions of the equation \(Rx^2 + Sy^2\equiv 1\pmod N\), On the parametrization of solutions of quadratic equations, Computing -series of geometrically hyperelliptic curves of genus three, Splitting full matrix algebras over algebraic number fields., Higher descents on an elliptic curve with a rational 2-torsion point, Computing the Cassels–Tate pairing on 3-isogeny Selmer groups via cubic norm equations, Trivializing a central simple algebra of degree 4 over the rational numbers., Brauer groups of diagonal quartic surfaces, Identifying the Matrix Ring: Algorithms for Quaternion Algebras and Quadratic Forms, Cyclic polygons with rational sides and area, Near-optimal parameterization of the intersection of quadrics. III. Parameterizing singular intersections, Algorithms for quadratic forms, Optimal affine reparametrization of rational curves, Solving quadratic equations using reduced unimodular quadratic forms, Selected Applications of LLL in Number Theory, How many rational points does a random curve have?, A parametric version of the Hilbert-Hurwitz theorem using hypercircles
Cites Work
- On the number of divisions of the Euclidean algorithm applied to Gaussian integers
- Small solutions of the Legendre equation
- Simultaneous representation of integers by a pair of ternary quadratic forms -- with an application to index form equations in quartic number fields
- On the passage from local to global in number theory
- An efficient solution of the congruence<tex>x^2 + ky^2 = mpmod{n}</tex>
- Notes on elliptic curves. II.
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item