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Aug 20 at 14:48 comment added user535671 @Wojowu hi! Thank you for your comment and for the reference you provided too. I'll take a look at it. It appears from your comment and Olivier's answer that I'll need to do things on an equation-by-equation basis. That's not the end of the world. I was just hoping for at least a yes to my question 3, as that would have made things much easier for my work. But thanks again. Your comment is helpful to me.
Aug 20 at 14:33 vote accept user535671
Aug 20 at 3:07 answer added Olivier timeline score: 4
Aug 19 at 19:43 comment added Wojowu I believe all results on strong BSD proceed by working $p$-adically, so all partial progress will proceed via (4). I believe this paper describes the state of the art of this result. It can probably be used to give examples for (2-a) and (3-b). FYI, the quotient $c(E)/c_1(E)$ is sometimes called the analytic order of Sha.
Aug 19 at 19:06 history edited user535671 CC BY-SA 4.0
edited title
Aug 19 at 18:03 history edited user535671 CC BY-SA 4.0
added Cassels-Tate pairing for why Sha(E) is a square
S Aug 19 at 13:21 review First questions
Aug 19 at 13:44
S Aug 19 at 13:21 history asked user535671 CC BY-SA 4.0