Specialization at T = 970/479 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -11140892170449903078832T^8 - 78517047092297850338880T^7 - 410980750922999091180480T^6 + 1172978174531038105951360T^5 + 202359376870041611948760T^4 + 727464198947794396860360T^3 - 533980972281075528757060T^2 - 2994527120513758550219760T - 1424568869019231533236800,
A6 = 466667176236662985209696435215744T^12 + 4902108138265145170676233713437440T^11 + 30904617405388839778675659644720640T^10 - 2235477311686016201360264232122880T^9 - 1928619458298746783809833278130720T^8 - 1321657250248806493665223528336049184T^7 + 1152166039831051025589342359093195760T^6 + 3336273056288691191096244581228211360T^5 - 1565104306692700007697832976891694060T^4 - 3952505302344716290555441880536817840T^3 + 26850110070164475305157052575243376T^2 + 1903147075480838773866179023498043520T + 656146040532506595230072169941913600.
It is a 2-neighbour of the fibration given in curve#3900: its Mordell-Weil lattice (rank 17, no reducible fibres) is a root-free Kneser 2-neighbour of that fibration's, realised by the pencil |O + P - F| for a section P of height 12. Constructed and searched by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.
apkorte ·