Specialization at T = -5/8 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -70456322121395744118987T^8 - 270736805521800700486056T^7 + 681665761636047060624T^6 + 1234481960342872464204384T^5 - 427072536207795566991240T^4 + 932522348198042719391664T^3 - 991232578762048531399536T^2 - 1438822739314664423398656T - 343540998025511181060672,
A6 = 7048126807600643691644744903627910T^12 + 41401267256924276544233395256738232T^11 + 51649295889445830016007199603753312T^10 - 208657301544441260965791912828085920T^9 - 522635766473158675684276944285342504T^8 + 252396058528754737573291576653064464T^7 + 2238764228696773065046286671966044432T^6 - 1352643968572944143440516173662043456T^5 - 2058834580016599491043353648535363824T^4 + 387649811099219784510189392096797440T^3 + 1175036907274176750041024493365538432T^2 + 525410171790549433434615584174902272T + 77513965269216205111736833614792960.
It is a 2-neighbour of the fibration given in curve#4187 (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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