Specialization at T = -653/146 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -1383044527665321116400T^8 - 16049999528139513071520T^7 + 15805299603407933138816T^6 + 712593854642478382322880T^5 - 3813994880887522829708400T^4 + 10533902963478229407850960T^3 - 10115880489507421099979016T^2 - 8597064026478854771701800T - 1511313760202147775869947,
A6 = 19606871590209659689292333520000T^12 + 323679316365878812163330339568000T^11 + 983969135059873668251937025883200T^10 - 6275524572874812809451065998804160T^9 - 65918284694373505756900522296861936T^8 - 337269555874810038655223788688478240T^7 + 5081060790854484290367532173908523840T^6 - 14611633213803604472414514215799717120T^5 + 11577647003766635578545334685110815264T^4 + 380100766090866777957899579121104880T^3 + 4610206606796227830325446909775634088T^2 + 8093183322260907342485075849728593400T + 2171157485142496238941816568266368214.
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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