Specialization at T = -1072/239 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -9326637192413076012400T^8 - 34884996069313200087200T^7 + 110925288656556862233440T^6 + 385813899399942596207360T^5 + 233890070443452935336560T^4 - 596691564815170847368240T^3 - 9841086512215258337654200T^2 - 7147300944594901868231960T - 1372341018983665060065307,
A6 = 355645975300077069151201411600000T^12 + 2273247912229167049862154805705600T^11 - 7137338446733984479207110102193984T^10 - 57261816964678192543182240688567360T^9 + 101108657979008556764293700373699600T^8 + 692858910748462408271944263396908640T^7 - 1034224818521729452686537198181505760T^6 - 4446809343349652848812523474435426752T^5 + 4366238810355442164044492645139162240T^4 + 13060804253335292158409237965744231280T^3 + 12512018819180205106449295745222847800T^2 + 4777750191287146089865021403646408520T + 622816136791651503989297338315313206.
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.
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