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

Acta Arithmetica (1997)

- Volume: 79, Issue: 4, page 333-352
- ISSN: 0065-1036

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topE. V. Flynn, and N. P. Smart. "Canonical heights on the Jacobians of curves of genus 2 and the infinite descent." Acta Arithmetica 79.4 (1997): 333-352. <http://eudml.org/doc/206982>.

@article{E1997,

author = {E. V. Flynn, N. P. Smart},

journal = {Acta Arithmetica},

keywords = {curves of genus two; Jacobians; canonical height; infinite descent; Mordell-Weil group; algorithm},

language = {eng},

number = {4},

pages = {333-352},

title = {Canonical heights on the Jacobians of curves of genus 2 and the infinite descent},

url = {http://eudml.org/doc/206982},

volume = {79},

year = {1997},

}

TY - JOUR

AU - E. V. Flynn

AU - N. P. Smart

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

JO - Acta Arithmetica

PY - 1997

VL - 79

IS - 4

SP - 333

EP - 352

LA - eng

KW - curves of genus two; Jacobians; canonical height; infinite descent; Mordell-Weil group; algorithm

UR - http://eudml.org/doc/206982

ER -

## References

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- [12] E. F. Schaefer, 2-descent on the Jacobians of hyperelliptic curves, J. Number Theory 51 (1995), 219-232. Zbl0832.14016
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- [14] S. Siksek, Infinite descent on elliptic curves, Rocky Mountain J. Math. 25 (1995), 1501-1538. Zbl0852.11028
- [15] J. H. Silverman, The Arithmetic of Elliptic Curves, Springer, 1986. Zbl0585.14026
- [16] J. H. Silverman, Computing heights on elliptic curves, Math. Comp. 51 (1988), 339-358. Zbl0656.14016
- [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] J. H. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves, Springer, 1994. Zbl0911.14015
- [19] J. H. Silverman, Computing canonical heights with little (or no) factorization, preprint, 1996.

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