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ECQ: implement change points according to curve model displayed#6855

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AndrewVSutherland merged 2 commits intoLMFDB:mainfrom
JohnCremona:ECQ_change_model
Feb 6, 2026
Merged

ECQ: implement change points according to curve model displayed#6855
AndrewVSutherland merged 2 commits intoLMFDB:mainfrom
JohnCremona:ECQ_change_model

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@JohnCremona
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This addresses #5326 . When you switch between the three available curve models (minimal, homogeneous, "simplified" = short Weierstrass) any points on the page (generators, torsion generators, integral points) change appropriately.

Clicking on the eye-con (top right) reveals raw text for the equation and integral points, but not yet for the generators, since I could not get that to work for entries in a table.

Implementation details: I enhanced the existing code which computes the simplified model to also return a function taking an affine point (x,y) on the original model to a point (x',y') on the simplified model. (This is the identity if a1=a3=0.) When points are retrived from the database (generators, torsion gens and integral points) they are mapped to projective points and affine points on the simplified model, so there are three versions of all the point lists.

I checked several examples but checking more would be useful. My test cases included 14a2 (a1 nonzero, rank 1), 20a4 (a1=a3=0, 5 integral points, rank 0), 916c1 (a1=a3=0, 22 integral points, rank 2). You need examples will positive rank and nontrivial torsion and some integral points, with both a1=a3=0 (so simplified already) and not.

@AndrewVSutherland
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I tried a bunch of random curves of varying positive rank and torsion, looks good!

@AndrewVSutherland AndrewVSutherland merged commit c19df33 into LMFDB:main Feb 6, 2026
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