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Some simple elliptic surfaces of genus zero

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References

  1. Bremner, A.: On elliptic surfaces of Mordell-Weil rank 4,Nagoya Math. J. 102, 101–115 (1986)

    MATH  MathSciNet  Google Scholar 

  2. Bremner, A.: On the equationy 2=x 3+k over function fields, Proc. NATO ASI, Banff, Alberta: Kluwer 1989

    Google Scholar 

  3. Cox, D.A., Zucker, S.: Intersection numbers of sections of elliptic surfaces,Invent. Math. 53, 1–44 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  4. Davenport, H.: Onf 3 (t)−g 2(t),Norske Vid. Selsk. Forh.,38, 86–87 (1965)

    MATH  MathSciNet  Google Scholar 

  5. Kodaira, K.: On compact analytic surfaces III,Ann. Math.,78, 1–40 (1963)

    Article  MathSciNet  Google Scholar 

  6. Lang, S.:Fundamentals of Diophantine Geometry, Wiley Interscience 1962

  7. Manin, Y.I.: The Tate height of points on an abelian variety. Its variants and applications, Izv. Akad. Nauk S.S.S.R., Ser. Mat.28, 1363–1390 (1964);A.M.S. Translations, Ser. 2,59, 82–110 (1966)

    MATH  MathSciNet  Google Scholar 

  8. Schwartz, C.: A Mordell-Weil group of rank 8 and a subgroup of finite index,Nagoya Math. J. 93, 19–26 (1984)

    MATH  MathSciNet  Google Scholar 

  9. Shioda, T.: On elliptic modular surfaces,J. Math. Soc. Japan 24, 20–57 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  10. Shioda, T.: The Galois Representations of TypeE 8 Arising from Certain Mordell-Weil Groups, Proc. Japan Acad.65A, 195–197 (1989)

    MathSciNet  Google Scholar 

  11. Shioda, T.: Mordell-Weil Lattices and Galois Representations I, II, III, Proc. Japan Acad.65A, 268–271; 296–299; 300–303 (1989)

    MathSciNet  Google Scholar 

  12. Silverman, J.H.: Computing heights on elliptic curves,Math. Comp. 51 (1988), 339–358

    Article  MATH  MathSciNet  Google Scholar 

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  1. Department of Mathematics, Arizona State University, 85287-1804, Tempe, AZ, USA

    Andrew Bremner

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  1. Andrew Bremner
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Bremner, A. Some simple elliptic surfaces of genus zero. Manuscripta Math 73, 5–37 (1991). https://doi.org/10.1007/BF02567626

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  • DOI: https://doi.org/10.1007/BF02567626

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