Specialization at T = 1050/61 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -9474380172051378777648T^8 + 143016499424841795151776T^7 - 978479134779758056367040T^6 + 1264156022749661958710016T^5 - 1005963702085547848031760T^4 - 1438422958271309512308048T^3 + 2172965217056038418681880T^2 + 1222317589612619797944408T - 1528603489372304441232027,
A6 = 356599201940399174539163794687872T^12 - 8095747446508036482913060524583296T^11 + 84031424784510859456436955014577216T^10 - 395756683659861170554655745272982720T^9 + 1041818162127380294010702794653004496T^8 - 91848543443162490589835301473411808T^7 - 1400855594533976892297125576033331840T^6 - 623560771669003657652924198286452928T^5 + 1801926810925269265387912620705751296T^4 + 1152132793779120258533624208322687440T^3 - 1448000646205536545177160777048329016T^2 - 809134531551941303559229668814825224T + 723128597502954965566093502187696054.
It is a 2-neighbour of the fibration given in curve#4205 (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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