Specialization at T = -181/119 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -16161338919951574537347T^8 - 183967925781776423843232T^7 - 306908503380230554874889T^6 + 1321820887548439573004394T^5 - 1089630203923766659668705T^4 + 1528127126557525645958556T^3 - 1325190033898795951823799T^2 - 1776684907545050991600198T - 509996388400821572993532,
A6 = 794074859864541402077984985828990T^12 + 13480216201562664173283363261525120T^11 + 58813044515050204101637768724085915T^10 - 27005959952131974781942342196787600T^9 - 297164658623174446064912117521429860T^8 - 610242665718369417817232061166604040T^7 + 2737840349733935589023201371120885290T^6 - 1476924630602948597826251203809007800T^5 - 1760224581565992882116105923868957910T^4 + 421401656201140614180762210583159560T^3 + 1429992029749290001354466937891106371T^2 + 752996037739894365105522529181137224T + 139570007340666087279594607715201844.
It is a 2-neighbour of the fibration given in curve#4191 (itself a 2-neighbour of the fibration 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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