Talk:Rank of an elliptic curve

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	This article was accepted from this draft on 5 August 2016 by reviewer Bilorv (talk · contribs).

Goldfeld conditional proof a bit narrower than stated

I removed a false bit from the opening section

" A claimed proof (assuming Birch–Swinnerton-Dyer conjecture mentioned above) by Alexander Smith has been posted in a preprint in 2017 on arXiv.^[1]^[2]^[3] "

The result in question is Cor 1.3, and assumes E has full rational 2-torsion and that E has no cyclic subgroup of order 4, in addition to BSD. In particular, it never proves Goldfeld's conjecture in general, even if BSD is proven. It seemed weird to have a conditional and partial proof in the opening section. If Goldfeld's conjecture gets a section, it would likely belong there. An Editor With a Self-Referential Name (talk) 06:40, 5 March 2019 (UTC)[reply]

References

^ Smith, Alexander. "2∞-Selmer groups, 2∞-class groups, and Goldfeld's conjecture". Retrieved 7 November 2018.
^ Smith, Alexander. "2∞-Selmer groups, 2∞-class groups, and Goldfeld's conjecture". Retrieved 7 November 2018.
^ Hartnett, Kevin. "New Proof Shows Infinite Curves Come in Two Types". Retrieved 7 November 2018.

Misleading lemma

Almost the complete article is not about the rank, but rather about the average rank. For example, the nonspecialist reader might not learn any ideas how to actually find the rank of a specific elliptic curve. Moreover, the last sentence of the intro (starting with “In other words” is not really an in-other-word. After all, an average of 1/2 would also be compatible with one with one third of the curves having rank 2 and the rest rank 0. 2A01:599:316:18E6:1477:5FA1:ADD2:BAF5 (talk) 16:29, 18 March 2024 (UTC)[reply]

[50-50-1] Smith, Alexander. "2∞-Selmer groups, 2∞-class groups, and Goldfeld's conjecture". Retrieved 7 November 2018.

[ias-2] Smith, Alexander. "2∞-Selmer groups, 2∞-class groups, and Goldfeld's conjecture". Retrieved 7 November 2018.

[quanta-3] Hartnett, Kevin. "New Proof Shows Infinite Curves Come in Two Types". Retrieved 7 November 2018.

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