Specialization at T = 271/34 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -80918153007142747807152T^8 + 354290935210738441284960T^7 + 117546745373133609199680T^6 - 1321723369189316995545600T^5 - 1222018032904985784972240T^4 - 1406850947577826580594160T^3 - 1254988108939355569153800T^2 + 805670525674002972117960T - 100416874821843548929275,
A6 = 8831810495179731787950781376781696T^12 - 58200269129275243642314244480725120T^11 + 52846203831582430953753256517509440T^10 + 303184046482963991294863102867915200T^9 - 457715356448899454589683173529277360T^8 - 744423311865278126846298019797769248T^7 + 1833256433177951161172716555006515840T^6 + 2794775310889560685872413753874966720T^5 - 133387102323757291083447813526175040T^4 - 778071888245494603901822019677467920T^3 + 439063195335888681561403448200034856T^2 - 128557299724393005377297960904774360T + 14412007642333428007694069449224150.
It is a 2-neighbour of the fibration given in curve#4205 (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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