Rank determines semi-stable conductor |
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Authors: | H. Kisilevsky |
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Affiliation: | Department of Mathematics and Statistics and CICMA, Concordia University, 1455 de Maisonneuve Blvd. West, Montréal, Quebec, Canada H3G 1M8 |
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Abstract: | Suppose that E1 and E2 are elliptic curves over the rational field, , such that for all quadratic fields . We prove that their conductors N(E1), and N(E2) are equal up to squares. If for all quadratic fields , then the same conclusion holds, provided the 2-parts of their Tate-Shafarevich groups are finite. |
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