Found by an independent search in the family y^2+a*x*y+b*y=x^3 with b=k^2-(a+1)*k, which contains the rational point (k,k) and the point (0,0) of order 3. Parameters a=-13, k=1079 give b=1177189, hence y^2-13*x*y+1177189*y=x^3. Submitted in its global minimal model [1,0,1,-7652324,346550615166]. PARI/GP ellrank returns bounds [5,5], proving rank exactly 5, and elltors returns invariant factors [3], proving torsion exactly Z/3Z. The five supplied rational points were computed by PARI and independently checked by the ICARM exact independence verifier.
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