Canonical heights on the Jacobians of curves of genus 2 and the infinite descent

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1. [1] J. W. S. Cassels, Lectures on Elliptic Curves, London Math. Soc. Stud. Texts 24, Cambridge University Press, 1991. Zbl0752.14033
2. [2] J. W. S. Cassels and E. V. Flynn, Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2, Cambridge University Press, 1996. Zbl0857.14018
3. [3] J. E. Cremona, Algorithms for Modular Elliptic Curves, Cambridge University Press, 1992. Zbl0758.14042
4. [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. Zbl0723.14023
5. [5] E. V. Flynn, The group law on the Jacobian of a curve of genus 2, J. Reine Angew. Math. 439 (1993), 45-69. Zbl0765.14014
6. [6] E. V. Flynn, Descent via isogeny in dimension 2, Acta Arith. 66 (1994), 23-43. Zbl0835.14009
7. [7] E. V. Flynn, An explicit theory of heights, Trans. Amer. Math. Soc. 347 (1995), 3003-3015. Zbl0864.11033
8. [8] E. V. Flynn, B. Poonen, and E. F. Schaefer, Cycles of quadratic polynomials and rational points on a genus 2 curve, preprint, 1996. Zbl0958.11024
9. [9] B. Gross, Local heights on curves, in: Arithmetic Geometry, G. Cornell and J. H. Silverman (eds.), Springer, 1986, 327-339. 
10. [10] S. Lang, Fundamentals of Diophantine Geometry, Springer, 1983. Zbl0528.14013
11. [11] M. Pohst and H. Zassenhaus, Algorithmic Algebraic Number Theory, Cambridge University Press, 1989. 
12. [12] E. F. Schaefer, 2-descent on the Jacobians of hyperelliptic curves, J. Number Theory 51 (1995), 219-232. Zbl0832.14016
13. [13] E. F. Schaefer, Class groups and Selmer groups, J. Number Theory 56 (1996), 79-114. Zbl0859.11034
14. [14] S. Siksek, Infinite descent on elliptic curves, Rocky Mountain J. Math. 25 (1995), 1501-1538. Zbl0852.11028
15. [15] J. H. Silverman, The Arithmetic of Elliptic Curves, Springer, 1986. Zbl0585.14026
16. [16] J. H. Silverman, Computing heights on elliptic curves, Math. Comp. 51 (1988), 339-358. Zbl0656.14016
17. [17] J. H. Silverman, The difference between the Weil height and the canonical height on elliptic curves, Math. Comp. 55 (1990), 723-743. Zbl0729.14026
18. [18] J. H. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves, Springer, 1994. Zbl0911.14015
19. [19] J. H. Silverman, Computing canonical heights with little (or no) factorization, preprint, 1996. 

1. Michael Stoll, On the height constant for curves of genus two
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