#3416: Weierstrass form and Jacobian for cubics and certain other genus-one
curves
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Reporter: moretti |
Owner: was
Type: enhancement |
Status: needs_review
Priority: major |
Milestone: sage-5.7
Component: elliptic curves |
Resolution:
Keywords: nagell, weierstrass, cubic, elliptic curves, editor_wstein |
Work issues:
Report Upstream: N/A |
Reviewers: John Cremona, Marco Streng, Nils Bruin
Authors: Niels Duif, Volker Braun |
Merged in:
Dependencies: #12553, #13084, #13458 |
Stopgaps:
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Comment (by vbraun):
I just want to point out that this is all more complicated and less
discoverable than just returning the morphism. Even if the function is not
called `Morphism_from_cubic_to_elliptic_curve` I think we are smart enough
to guess what the result means.
For the record, this is the current state:
* `EllipticCurve(x^3+y^3+z^3, [1,-1,0])` returns elliptic curve
* `EllipticCurve_from_cubic(x^3+y^3+z^3, [1,-1,0])` returns morphism
* `EllipticCurve_from_cubic(x^3+y^3+z^3, [1,-1,0], morphism=True)` returns
morphism
* `EllipticCurve_from_cubic(x^3+y^3+z^3, [1,-1,0], morphism=False)`
returns elliptic curve
* `Jacobian(x^3+y^3+z^3)` returns elliptic curve
* `Jacobian(x^3+y^3+z^3, morphism=False)` returns elliptic curve
* `Jacobian(x^3+y^3+z^3, morphism=True)` returns morphism (but not
isomorphism)
We can always tack on defining data to the elliptic curve in another
ticket, so imho the only discussion that is relevant to this ticket is
whether `morphism` should default to true or false.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/3416#comment:63>
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