>>278
>有理数体 Q 上で考えた場合、正確なランクが判明している楕円曲線のうち、最大のランクを持つ楕円曲線は、2009年にノーム・エルキース（英語版）により発見された
>y2 + xy + y = x3 - x2 + 31368015812338065133318565292206590792820353345x + 302038802698566087335643188429543498624522041683874493555186062568159847
>であり、そのランクは 19 である[11]。

英文wikipediaでは、ランク20 by Noam Elkies and Zev Klagsbrunの記載があるね
あと、Notesで、NagaoとNagao - Kouyaが出てくるけど、はて？（＾＾；

（参考）
https://en.wikipedia.org/wiki/Elliptic_curve
Elliptic curve

The elliptic curve with biggest exactly known rank is
y2 + xy + y = x3 - x2 - 244537673336319601463803487168961769270757573821859853707x + 961710182053183034546222979258806817743270682028964434238957830989898438151121499931
It has rank 20, found by Noam Elkies and Zev Klagsbrun in 2020.[4]

Notes
4 https://web.math.pmf.unizg.hr/~duje/tors/rankhist.html
Dujella, Andrej. "History of elliptic curves rank records". University of Zagreb.

The "folklore" conjecture is that a rank can be arbitrary large. However there are also recent heuristic arguments that suggest the boundedness of the rank of elliptic curves.

The highest rank of an elliptic curve which is (unconditionally) known exactly (not only a lower bound for rank) is equal to 20, and it is found by Elkies-Klagsbrun in 2020.

The following table contains some historical data on elliptic curve rank records.
________________________________________________________________________________
rank >= year Author(s)
17 1992 Nagao
20 1993 Nagao
21 1994 Nagao - Kouya