Specialization at T = 2/5 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -129423262682594003679387T^8 + 364444960853480119379208T^7 + 145088936906457036995136T^6 - 946405361864597551050816T^5 + 1086632441482958356509720T^4 - 615454597853371985855184T^3 - 2089672621773109442565264T^2 + 1503858169634937349756032T - 268043453574349038086592,
A6 = 22378678518203765279639595291703734T^12 - 97642937907003790975195419097186584T^11 - 57701568157490976356217548246274864T^10 + 692728062356311676289756774010506240T^9 - 165059119295086271477298303488050440T^8 - 2065127205357525454766777049159397680T^7 + 866901377553305534044230525750471600T^6 + 2900595200522009433908965902519647040T^5 - 1511852767062133534934112666639840240T^4 - 1121738997234616988726901721424515200T^3 + 1300199883149489416130125996732379520T^2 - 448873241175573293059242892011302400T + 53141649442568035635166156713288960.
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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