Specialization at T = -337/2 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -11871310334515632T^8 + 4710110008611306816T^7 - 2086020069231986711136T^6 - 184523251173755635536480T^5 - 6701046568565117730395760T^4 - 153188863150147099034594256T^3 - 1728397061227994797149412104T^2 + 1293824158270290221749735140T - 3009001448051781638619102975,
A6 = 425207191402126274866560T^12 - 563052339092973212554731264T^11 + 242123500866097746692387835264T^10 + 23032729293888429602372703530880T^9 + 3121622944690084624163225355490944T^8 + 295262495155831884321522320323442496T^7 + 13000284347332506536750445881902721952T^6 + 266703534992086688942874014282698665168T^5 + 2231811615310432924685764525429401885924T^4 + 6596027232624269118843692038876188450360T^3 + 95451184990094031890361698435840315288700T^2 - 68941255711464655644860348072488527433500T + 38303805195121251570249945560744186021250.
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.
apkorte ·