Computing heights on elliptic curves

Mathematics of Computation

Volumn 51, Issue 183, 1988, Pages 339-358

  Silverman, Joseph H ^a  

^a BOSTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84968504366     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1988-0942161-4     Document Type: Article

References (19)

1. J. P. BUHLER, B. H. GROSS & D. B. Zagier, "On the conjecture of Birch and Swinnerton- Dyer for an elliptic curve of rank 3, " Math.Comp., v. 44, 1985, pp. 473-481.
2. D. Cox ¿i S. ZUCKER, "Intersection numbers of sections of elliptic surfaces, " Invent. Math., v. 53, 1979, pp. 1-44.
3. P. Deligne, "Courbes Elliptiques: Formulaire (d'après J. Täte), " in Modular Functions of One Variable IV, Lecture Notes in Math., vol. 476, Springer-Verlag, Berlin and New York, 1975, pp. 53-74.
4. B. H. GROSS, "Local heights on curves, " in Arithmetic Geometry, Springer-Verlag, Berlin and New York, 1986, pp. 327-340.
5. B. H. GROSS & D. B. Zagier, "Heegner points and derivatives of L-series, " Invent. Math., v. 84, 1986, 225-320.
6. S. LANG, Elliptic Curves: Diophantine Analysis, Springer-Verlag, Berlin and New York, 1978.
7. S. LANG, Fundamentals of Diophantine Geometry, Springer-Verlag, Berlin and New York, 1983.
8. M. LASKA, "An algorithm for finding a minimal Weierstrass equation for an elliptic curve, " Math. Comp., v. 38, 1982, pp. 257-260.
9. D. MASSER & G. WÜSTHOLZ, "Fields of large transcendence degree generated by values of elliptic functions, " Invent. Math., v. 72, 1983, pp. 407-464.
10. J. H. SILVERMAN, The Neron-Tate Height on Elliptic Curves, Ph.D. thesis, Harvard, 1981.
11. J. H. SILVERMAN, The Arithmetic of Elliptic Curves, Graduate Text 106, Springer, New York, 1986.
12. J. H. SILVERMAN, "A quantitative version of Siegel's theorem, " J. Reine Angew. Math., v. 378, 1987, pp. 60-100.
13. J. H. SILVERMAN, Elliptic Curve Calculator v. 5.05, a program for the Apple Macintosh computer, 1987.
14. J. T. TÄTE, "Algorithm for finding the type of a singular fibre in an elliptic pencil, " in Modular Functions of One Variable IV, Lecture Notes in Math., vol. 476, Springer-Verlag, Berlin and New York, 1975, pp. 33-52.
15. J. T. TÄTE, Letter to J. P. Serre, Oct. 1, 1979.
16. H. M. TSCHÖPE & H. G. ZIMMER, "Computation of the Néron-Tate height on elliptic curves, " Math. Comp., v. 48, 1987, pp. 351-370.
17. B. L. VAN DER WAERDEN, Algebra, 7th ed., Ungar, New York, 1970.
18. D. B. ZAGIER, "Large integral points on curves, " Math. Comp., v. 48, 1987, pp. 425-436
19. H. G. ZIMMER, "Quasifunctions on elliptic curves over local fields, " J. Reine Angew. Math., v. 307, 308, 1979, pp. 221-246;