Tighten 2-isogeny descent local solubility checks (improve rank upper bounds)#5
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asiryan wants to merge 3 commits into
Open
Tighten 2-isogeny descent local solubility checks (improve rank upper bounds)#5asiryan wants to merge 3 commits into
asiryan wants to merge 3 commits into
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Motivation
RankBounds/TwoIsogenySelmerDimension(partial improvement toward a full descent implementation).Description
sources/EllipticCurveQ.Analysis.cs.intwith an explicit loop that filters out p<2 and returnsnullif any prime exceedsint.MaxValue, avoiding unsafe casts.HasSolutionModuloPrimeto check solvability modulop(and handle singular roots via a lift top^2).p | din the quartic by reducing the equation and checking the correct residue classes; addIsSquareInQpto detect trivial solvability via aQ_psquare test forb/d.2^6(64) to2^8(256) to reduce missed 2-adic obstructions; add helpersModToLong/ reuseModToIntfor safe modular reductions.Testing
dotnet build, execute theexamplesprogram, and compareRankBoundsresults on known curves against trusted data (e.g. LMFDB) to verify improved upper bounds.Notes: this PR tightens local solubility checks used in the 2-isogeny descent and should reduce false-positive Selmer classes; it is not a complete implementation of all descent methods (full multi-descent / global 2-descent is not yet implemented).
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