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Computations on an equation of the birch and swinnerton-dyer type

Francisco X. Portillo-Bobadilla, Felipe Voloch, John Tate

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Abstract

Let us assume that E/Q is an elliptic curve of level N and rank equal to 1. Let q be a prime that does not divide the conductor. We study conjecture 4 of B. Mazur and J. Tate in [MT87]. This conjecture relates to the Birch and Swinnerton-Dyer problem in the q-adic case. We produce a lot of numerical evidence towards the conjecture. We also propose a refinement of the conjecture in the rank 1 case in section 2.3.

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Let us assume that E/Q is an elliptic curve of level N and rank equal to 1. Let q be a prime that does not divide the conductor. We study conjecture 4 of B. Mazur and J. Tate in [MT87]. This conjecture relates to the Birch and Swinnerton-Dyer problem in the q-adic case. We produce a lot of numerical evidence towards the conjecture. We also propose a refinement of the conjecture in the rank 1 case in section 2.3.

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Let us assume that E/Q is an elliptic curve of level N and rank equal to 1. Let q be a prime that does not divide the conductor. We study conjecture 4 of B. Mazur and J. Tate in [MT87]. This conjecture relates to the Birch and Swinnerton-Dyer problem in the q-adic case. We produce a lot of numerical evidence towards the conjecture. We also propose a refinement of the conjecture in the rank 1 case in section 2.3.

Key concepts: Conjecture, Rank (graph theory), Elliptic curve, Prime (order theory), Mathematics, Type (biology), Combinatorics, Computation

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