Evans Triangles and Edwards Curves

Wensen Wu The Affiliated High School of SCNU

S.-T. Yau High School Science Awarded Papers mathscidoc:1801.35002

Yau Science Award (Math), 2017.12
We reduced the unsolved problem of Evans triangles to the problem of nding rational points on a class of elliptic curves, the twisted Edwards curves En. We proved that the set of all Evans triangles with a given ratio is isomorphic to a quotient group of En(Q). After this, using Sage, we can solve the Evans problem for an amount of cases within the capacity of computer. Even without the help of a computer, we can still obtain a large class of new Evans triangles, and nd an e ective way to test if the rank of an Edwards curve is positive or not.
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@inproceedings{wensen2017evans,
  title={Evans Triangles and Edwards Curves},
  author={Wensen Wu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180113194414598184875},
  booktitle={Yau Science Award (Math)},
  year={2017},
}
Wensen Wu. Evans Triangles and Edwards Curves. 2017. In Yau Science Award (Math). http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180113194414598184875.
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