# Arithmetic and geometry of the curve y³+1=x⁴

Matthew J. Klassen; Edward F. Schaefer

Acta Arithmetica (1996)

- Volume: 74, Issue: 3, page 241-257
- ISSN: 0065-1036

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topMatthew J. Klassen, and Edward F. Schaefer. "Arithmetic and geometry of the curve y³+1=x⁴." Acta Arithmetica 74.3 (1996): 241-257. <http://eudml.org/doc/206850>.

@article{MatthewJ1996,

author = {Matthew J. Klassen, Edward F. Schaefer},

journal = {Acta Arithmetica},

keywords = {Jacobian variety; quartic curve; Weierstrass points; Mordell-Weil group; isogeny; CM elliptic curve},

language = {eng},

number = {3},

pages = {241-257},

title = {Arithmetic and geometry of the curve y³+1=x⁴},

url = {http://eudml.org/doc/206850},

volume = {74},

year = {1996},

}

TY - JOUR

AU - Matthew J. Klassen

AU - Edward F. Schaefer

TI - Arithmetic and geometry of the curve y³+1=x⁴

JO - Acta Arithmetica

PY - 1996

VL - 74

IS - 3

SP - 241

EP - 257

LA - eng

KW - Jacobian variety; quartic curve; Weierstrass points; Mordell-Weil group; isogeny; CM elliptic curve

UR - http://eudml.org/doc/206850

ER -

## References

top- [C1] R. Coleman, Torsion points on curves and p-adic Abelian integrals, Ann. of Math. 121 (1985), 111-168. Zbl0578.14038
- [C2] R. Coleman, Torsion points on Abelian etale coverings of P¹-{0,1,∞}, Trans. Amer. Math. Soc. 311 (1989), 185-208.
- [F] D. K. Faddeev, Group of divisor classes on the curve defined by the equation x⁴+y⁴=1, Soviet Math. Dokl. 1 (1960), 1149-1151. Zbl0100.03401
- [H] R. Hartshorne, Algebraic Geometry, Springer, New York, 1977.
- [KS] M. J. Klassen and E. F. Schaefer, Group law and descent on smooth plane quartics, preprint.
- [L] J. Lewittes, Automorphisms of compact Riemann surfaces, Amer. J. Math. 85 (1963), 734-752. Zbl0146.10403
- [Ma] A. Mattuck, Abelian varieties over p-adic ground fields, Ann. of Math. 62 (1955), 92-119. Zbl0066.02802
- [Mi] J. S. Milne, Jacobian varieties, in: Arithmetic Geometry, G. Cornell and J. H. Silverman (eds.), Springer, New York, 1986, 167-212.
- [V] A. M. Vermeulen, Weierstrass points of weight two on curves of genus three, Ph.D. Thesis, University of Amsterdam, 1983. Zbl0534.14010

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