Specialization at T = 253/2 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -7016388255537308794800T^8 - 178679712000491349877440T^7 - 1393427674620775645747200T^6 - 570182635321524575663040T^5 - 753965899387475415418440T^4 - 320804658906630906472920T^3 + 1134421125068367717675300T^2 + 399978175235844546966960T - 422082632478729918479472,
A6 = 219688715864979146315449005782400T^12 + 6098200250797428195163726469525760T^11 + 54477207303588087906057214569267456T^10 + 264783925318167622977267944863123200T^9 + 1702978825713300190413814657041122400T^8 + 932916852969092429403286366085219040T^7 - 1775033404268099174843557641423862320T^6 - 1248513743927587153502730303378288864T^5 + 1060720915885228836685362726021218580T^4 + 675987962412402587067553913812781760T^3 - 432422499228520607079300144749998800T^2 - 178229177722910279472469086969305280T + 105716686434811400528878525349249664.
It is a 2-neighbour of another fibration built here (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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