cannot be modular.<ref name="ribet">{{cite journal sfn|last=Ribet|first=Ken |author-link=Ken Ribet |title=On modular representations of Gal({{overline|'''Q'''}}/'''Q''') arising from modular forms |journal=Inventiones Mathematicae |volume=100 |year=1990 |issue=2 |pages=431–476 |doi=10.1007/BF01231195 |mr=1047143 |url=https://math.berkeley.edu/~ribet/Articles/invent_100.pdf |hdl=10338.dmlcz/147454 |bibcode=1990InMat.100..431R |s2cid=120614740 }}</ref> Thus, the proof of the Taniyama–Shimura–Weil conjecture for this family of elliptic curves (called Hellegouarch–Frey curves) implies FLT. The proof of the link between these two statements, based on an idea of [[Gerhard Frey]] (1985), is difficult and technical. It was established by [[Kenneth Ribet]] in 1987.<ref>See the survey of {{cite journal |first=K. |last=Ribet |title=From the Taniyama–Shimura conjecture to Fermat's Last Theorem |journal=Annales de la Faculté des Sciences de Toulouse |volume=11 |year=19901990b |pages=116–139 |doi= 10.5802/afst.698|url=http://www.numdam.org/item?id=AFST_1990_5_11_1_116_0 |doi-access=free }}</ref>
