---
title: "Bibliography"
canonical: "https://docs.magma-maths.org/ArithmeticGeometry/ModelsOfGenusOneCurves/bibliography.html"
source: "https://docs.magma-maths.org/ArithmeticGeometry/ModelsOfGenusOneCurves/bibliography.md"
part: "Arithmetic Geometry"
chapter: "Models of Genus One Curves"
breadcrumbs:
  - {"title": "Magma Handbook", "source": "../../index.md"}
  - {"title": "Arithmetic Geometry", "source": "../index-arithmetic-geometry.md"}
  - {"title": "Models of Genus One Curves", "source": "index-models-of-genus-one-curves.md"}
prev: {"title": "Examples", "source": "extended-examples.md"}
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---

# Bibliography

<a id="cite-six-authors-invariants"></a>
- **[AKM+01]** Sang Yook An, Seog Young Kim, David C. Marshall, Susan H. Marshall, William G. McCallum, and Alexander R. Perlis. Jacobians of genus one curves. *J. Number Theory*, 90(2):304–315, 2001.
<a id="cite-artin-etal"></a>
- **[ARVT05]** Michael Artin, Fernando Rodriguez-Villegas, and John Tate. On the Jacobians of plane cubics. *Adv. Math.*, 198(1):366–382, 2005.
<a id="cite-cremona-fisher-stoll"></a>
- **[CFS10]** J.E. Cremona, T.A Fisher, and M Stoll. Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves. *Algebra & Number Theory*, 4(6):763–820, 2010.
<a id="cite-mazur-cremona"></a>
- **[CM00b]** John E. Cremona and Barry Mazur. Visualizing elements in the Shafarevich-Tate group. *Experiment. Math.*, 9(1):13–28, 2000.
<a id="cite-fisher-invariants"></a>
- **[Fis08a]** T.A Fisher. The invariants of a genus one curve. *Proc. Lond. Math. Soc.*, 97(3):753–782, 2008.
<a id="cite-fisher"></a>
- **[Fis06a]** T.A. Fisher. Testing equivalence of ternary cubics. In S. Pauli F. Hess and M.Pohst, editors, *ANTS VII*, volume 4076 of LNCS, 333–345. Springer-Verlag, 2006.
<a id="cite-fisher-hessian"></a>
- **[Fis06b]** Tom Fisher. The Hessian of a genus one curve. preprint arXiv:math/0610403v2 [math.NT], 2006.
<a id="cite-rubin-silverberg"></a>
- **[RS95]** K. Rubin and A. Silverberg. Families of elliptic curves with constant mod $p$ representations. In *Elliptic curves, modular forms, & Fermat's last theorem (Hong Kong, 1993)*, Ser. Number Theory, I, pages 148–161. Internat. Press, Cambridge, MA, 1995.