Specialization at T = 5934/4651 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -76081088435681081513047T^8 + 352756680332626657087252T^7 - 82339513624259414646469T^6 - 901545658338022693466490T^5 + 229450949582480650416915T^4 - 1247200030321945517143512T^3 - 1146369340545356004506811T^2 + 1687352936729813079668190T - 411496468647819081255900,
A6 = 8112841022538000650593845586374970T^12 - 57168146144925559393934264903441092T^11 + 74672050992321347131912066302099019T^10 + 277662613390589143744390101854640120T^9 - 608279964343956992513678172184166364T^8 - 775627450421715998790683046858185472T^7 + 1913663946413950754123492444913586362T^6 + 1711261933991806885632762747792403176T^5 - 2007957630504188399500442532556750554T^4 - 505502209838775107774478816852469020T^3 + 1225508258092292403296873724948672675T^2 - 576830173318718574016743233507280000T + 96363113602603152516124313597692500.
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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