Found by an independent specialization search in the rank-at-least-1 family from Leopoldo Kulesz, Families of elliptic curves of high rank with nontrivial torsion group over Q, Acta Arithmetica 108 (2003), Theorem 2.6: https://www.impan.pl/shop/en/publication/transaction/download/product/82638 . At u=13/17, the Tate parameter is t=-2*(u-3)/(u^2+3)=323/259. The curve y^2+(1-c)xy-by=x^3-bx^2, where b=t^2*(t-1) and c=t*(t-1), is submitted in its global minimal model. PARI/GP ellrank returns bounds [4,4], proving rank exactly 4, and elltors returns invariant factors [7], proving torsion exactly Z/7Z. The four supplied rational points were computed by PARI and independently checked by the ICARM exact independence verifier.
David Renshaw ·