On the distribution of analytic ranks of elliptic curves

Mestre's Finite Field Method for Searching Elliptic Curves with High Ranks

“…Recent research in rank studies has tackled three key areas: calculating ranks for specific families of curves [15][16][17][18][19], exploring how rank behaves for curves constructed from special number sequences [20][21][22][23][24][25][26][27][28] and analyzing rank distributions within families and across field extensions [29][30][31]. Dujella [32] provided an enumeration of the strategies for generating high-rank Diaphontine elliptic curves.…”