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Generalize the division_field method of elliptic curve to the composite case #24340

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kevinywlui mannequin opened this issue Dec 8, 2017 · 1 comment · Fixed by #35936
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Generalize the division_field method of elliptic curve to the composite case #24340

kevinywlui mannequin opened this issue Dec 8, 2017 · 1 comment · Fixed by #35936
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c: elliptic curves p: major / 3 t: enhancement
Milestone
sage-10.3

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@kevinywlui
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kevinywlui mannequin commented Dec 8, 2017

For an elliptic curve E, a natural number n, and a number field K, the n-division field of E over K is the smallest extension of K that contains all the coordinates of the n-torsion subgroup.

Currently, only the prime case is implemented. This ticket aims to implement the composite case.

There's also a small typo in the proof of the theorem within the current code (L501 of ell_number_field.py) that should be fixed.

Component: elliptic curves

Keywords: division field

Branch: u/klui/generalize_the_division_field_method_of_elliptic_curve_to_the_composite_case

Issue created by migration from https://trac.sagemath.org/ticket/24340
@kevinywlui kevinywlui mannequin added this to the sage-8.2 milestone Dec 8, 2017
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kevinywlui mannequin commented Feb 1, 2018

Branch: u/klui/generalize_the_division_field_method_of_elliptic_curve_to_the_composite_case

@mkoeppe mkoeppe removed this from the sage-8.2 milestone Dec 29, 2022
@yyyyx4 yyyyx4 mentioned this issue Dec 3, 2023
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vbraun pushed a commit to vbraun/sage that referenced this issue Dec 4, 2023
sagemathgh-35936: generalize EllipticCurve_field.division_field() to …
36e2a1c 
…composite orders

    
The `.division_field()` method is currently restricted to prime orders
for no serious reason. This patch makes it work for composite orders,
generalizing [an observation of @JohnCremona](https://github.com/sagemat
h/sage/issues/11905#issuecomment-1417417647) in the process.

Note: I'm not sure if this is the optimal approach. I also played around
with building the extension as a tower corresponding to the
factorization of $n$, but (at least in Sage) it seemed significantly
slower than the version here.

Fixes sagemath#24340.
    
URL: sagemath#35936
Reported by: Lorenz Panny
Reviewer(s): John Cremona
vbraun pushed a commit to vbraun/sage that referenced this issue Dec 5, 2023
sagemathgh-35936: generalize EllipticCurve_field.division_field() to …
b60398e 
…composite orders

    
The `.division_field()` method is currently restricted to prime orders
for no serious reason. This patch makes it work for composite orders,
generalizing [an observation of @JohnCremona](https://github.com/sagemat
h/sage/issues/11905#issuecomment-1417417647) in the process.

Note: I'm not sure if this is the optimal approach. I also played around
with building the extension as a tower corresponding to the
factorization of $n$, but (at least in Sage) it seemed significantly
slower than the version here.

Fixes sagemath#24340.
    
URL: sagemath#35936
Reported by: Lorenz Panny
Reviewer(s): John Cremona
@mkoeppe mkoeppe added this to the sage-10.3 milestone Dec 6, 2023
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generalize EllipticCurve_field.division_field() to composite orders yyyyx4/sage
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