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Jan 1, 2022 at 20:10 comment added Stanley Yao Xiao @lalala one would arrive at that conclusion by considering the so-called parity conjecture and the minimalist conjecture. The former asserts that the parity of the rank of elliptic curves should not be biased towards odd or even, so half the time the rank should be even and the other half of the time it should be odd. The minimalist conjecture asserts that ranks are as low as they need to be, which means that half the time they should be 0 and the other half of the time it should be 1. Combining these assertions gives that the rank should be 1/2 on average.
Jan 1, 2022 at 10:26 comment added lalala So how did anybody guess the conjecture in the first place?
Dec 30, 2021 at 21:32 history edited Stanley Yao Xiao CC BY-SA 4.0
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Dec 29, 2021 at 23:05 comment added Chris Wuthrich Here some historic evidence that the heuristic question was discussed, but wasn't settled by 2006.
Dec 29, 2021 at 20:36 history made wiki Post Made Community Wiki by Stefan Kohl
Dec 29, 2021 at 19:44 history answered Stanley Yao Xiao CC BY-SA 4.0