Abstract
We try to find all the elliptic curves over Q, up to isomorphism, with non-degenerate reduction at all primes except 2 or 3 primes possessing a rational point of finite order by making use of some diophantine equations.
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BERGMAI, G.: On the exceptional points of cubic curves. Ark. för Mat.2, 489–535 (1953)
BIRCH, B. J. and KUYK, W. (eds.): Modular functions of one variable IV. Lecture Notes in Math.476, Berlin-Heidelberg-New York: Springer, 1975
DICKSON, L. E.: History of the theory of numbers, Vol. II, New York: Chelsea, 1971
HADANO, T.: On the conductor of an elliptic curve with a rational point of order 2. Nagoya Math. J.53, 199–210 (1974)
HADANO, T.: Elliptic curves with a torsion point. Nagoya Math. J.66, 99–108 (1977)
HADANO, T.: L'exposant en 2 du conducteur de la courbe elliptique y2+x3+ax+b=0. Reports Fac. Sci. and Technol. Meijō Univ.18, 120–122 (1978)
MAZUR, B.: Modular curves and the Eisenstein ideal. Publ. Math. I. H. E. S.47, 35–193 (1978)
MORDELL, L. J.: Diophantine equations. London-New York: Academic Press, 1969
OGG, A. P.: Abelian curves of small conductor. J. Reine Angew. Math.226, 204–215 (1967)
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Hadano, T. Elliptic curves with a rational point of finite order. Manuscripta Math 39, 49–79 (1982). https://doi.org/10.1007/BF01312445
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DOI: https://doi.org/10.1007/BF01312445