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Elliptic curves maximal over extensions of finite base fields
- Source :
- Mathematics of Computation, 88(315), 453-465. AMER MATHEMATICAL SOC
- Publication Year :
- 2019
- Publisher :
- AMER MATHEMATICAL SOC, 2019.
-
Abstract
- Given an elliptic curve E over a finite field F-q we study the finite extensions F(q)n of F-q such that the number of F(q)n-rational points on E attains the Hasse upper bound. We obtain an upper bound on the degree n for E ordinary using an estimate for linear forms in logarithms, which allows us to compute the pairs of isogeny classes of such curves and degree n for small q. Using a consequence of Schmidt's Subspace Theorem, we improve the upper bound to n
- Subjects :
- Isogeny
Pure mathematics
Algebra and Number Theory
Subspace theorem
Degree (graph theory)
Logarithm
Applied Mathematics
010102 general mathematics
010103 numerical & computational mathematics
01 natural sciences
Upper and lower bounds
Base (group theory)
Computational Mathematics
Elliptic curve
Finite field
0101 mathematics
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 00255718
- Volume :
- 88
- Issue :
- 315
- Database :
- OpenAIRE
- Journal :
- Mathematics of Computation
- Accession number :
- edsair.doi.dedup.....f8bcbe929c4f8e9947e19ed132e57598