Found by an independent rational-parameter search in the Tate family y^2+(1-t)xy-ty=x^3-tx^2 at t=119/172, whose point (0,0) has order 5. Submitted in the global minimal model [1,1,1,-223521435,1911696935401]. PARI/GP ellrank returns bounds [4,4], proving rank exactly 4, and elltors returns invariant factors [5], proving torsion exactly Z/5Z. The four supplied rational points were found by PARI and independently checked by the ICARM exact independence verifier.
David Renshaw ·