@article{bwmeta1.element.bwnjournal-article-aav79i4p333bwm, author = {E. V. Flynn and N. P. Smart}, title = {Canonical heights on the Jacobians of curves of genus 2 and the infinite descent}, journal = {Acta Arithmetica}, volume = {80}, year = {1997}, pages = {333-352}, zbl = {0895.11026}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav79i4p333bwm} }
E. V. Flynn; N. P. Smart. Canonical heights on the Jacobians of curves of genus 2 and the infinite descent. Acta Arithmetica, Tome 80 (1997) pp. 333-352. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav79i4p333bwm/
[000] [1] J. W. S. Cassels, Lectures on Elliptic Curves, London Math. Soc. Stud. Texts 24, Cambridge University Press, 1991. | Zbl 0752.14033
[001] [2] J. W. S. Cassels and E. V. Flynn, Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2, Cambridge University Press, 1996. | Zbl 0857.14018
[002] [3] J. E. Cremona, Algorithms for Modular Elliptic Curves, Cambridge University Press, 1992. | Zbl 0758.14042
[003] [4] E. V. Flynn, The Jacobian and formal group of a curve of genus 2 over an arbitrary ground field, Proc. Cambridge Philos. Soc. 107 (1990), 425-441. | Zbl 0723.14023
[004] [5] E. V. Flynn, The group law on the Jacobian of a curve of genus 2, J. Reine Angew. Math. 439 (1993), 45-69. | Zbl 0765.14014
[005] [6] E. V. Flynn, Descent via isogeny in dimension 2, Acta Arith. 66 (1994), 23-43. | Zbl 0835.14009
[006] [7] E. V. Flynn, An explicit theory of heights, Trans. Amer. Math. Soc. 347 (1995), 3003-3015. | Zbl 0864.11033
[007] [8] E. V. Flynn, B. Poonen, and E. F. Schaefer, Cycles of quadratic polynomials and rational points on a genus 2 curve, preprint, 1996. | Zbl 0958.11024
[008] [9] B. Gross, Local heights on curves, in: Arithmetic Geometry, G. Cornell and J. H. Silverman (eds.), Springer, 1986, 327-339.
[009] [10] S. Lang, Fundamentals of Diophantine Geometry, Springer, 1983. | Zbl 0528.14013
[010] [11] M. Pohst and H. Zassenhaus, Algorithmic Algebraic Number Theory, Cambridge University Press, 1989.
[011] [12] E. F. Schaefer, 2-descent on the Jacobians of hyperelliptic curves, J. Number Theory 51 (1995), 219-232. | Zbl 0832.14016
[012] [13] E. F. Schaefer, Class groups and Selmer groups, J. Number Theory 56 (1996), 79-114. | Zbl 0859.11034
[013] [14] S. Siksek, Infinite descent on elliptic curves, Rocky Mountain J. Math. 25 (1995), 1501-1538. | Zbl 0852.11028
[014] [15] J. H. Silverman, The Arithmetic of Elliptic Curves, Springer, 1986. | Zbl 0585.14026
[015] [16] J. H. Silverman, Computing heights on elliptic curves, Math. Comp. 51 (1988), 339-358. | Zbl 0656.14016
[016] [17] J. H. Silverman, The difference between the Weil height and the canonical height on elliptic curves, Math. Comp. 55 (1990), 723-743. | Zbl 0729.14026
[017] [18] J. H. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves, Springer, 1994. | Zbl 0911.14015
[018] [19] J. H. Silverman, Computing canonical heights with little (or no) factorization, preprint, 1996.