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We give an algorithm that, for an elliptic curve E over ℚ̅ in Weierstraß form, computes the infimum and supremum of the difference between the naïve and canonical height functions on E(ℚ̅).
In this expository note, we describe an arithmetic pairing associated to an isogeny between Abelian varieties over a finite field. We show that it generalises the Frey–Rück pairing, thereby giving a short proof of the perfectness of the latter.
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