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BSD is true for 141a

Summary of Proof:

  1. For p=2 : Cremona verified this several years ago via a 2 -descent.

  2. For all p3  with p==7 : Kolyvagin's bound implies that p=j#Sha(E) .

  3. For p=7 : we computed the 7 -adic regulator, found that it was nonzero. Then using that the mod-7  representation is surjective, the bounds coming from Iwasawa theory, and thoerems of Kato, Perrin-Riou, Schneider, and others imply that ord7(Sha(E))=0 .

  4. We conclude that the full BSD conjecture is true for the elliptic curve 141a.

Key Point

Applying the general theory is now fairly straightforward. Combining together the wide range of theorems people have proved toward BSD gives quite a lot, and illustrates and motives work to fill in the remaining gaps.

NEXT: Summary of Results and The Goal

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