Abstract
For an elliptic curve over the rationals, optimal in its isogeny class, with a rational point of order 7 but L E (1) ≠ 0, we prove that 7 divides the product of the Tamagawa factors with the order of the Shafarevich-Tate group. This is a small consequence of the Birch and Swinnerton-Dyer conjecture.
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