I provide a systematic construction of points (defined over a large number fields) on the Legendre curve over Q: for any odd integer n ≥ 3 my method constructs n points on the Legendre curve and I show that rank of the subgroup of the Mordell-Weil group they generate is n if n ≥ 7. I also show that every elliptic curve over any number field admits similar type of points after a finite base extension.
|Original language||English (US)|
|State||Published - May 21 2017|
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