Specialization at T = 19/33 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -6195147929170777488267T^8 - 76325725939813122988800T^7 - 882325168895840084876340T^6 + 137101400449928233205328T^5 - 540371179907883674625330T^4 + 1432666851749665397357472T^3 + 819022076707710173673708T^2 - 1550804727906185486991696T - 817873967341793893325067,
A6 = 184510578295520929147533147781830T^12 + 3583110577624752524437698479790336T^11 + 53501492723177054560052620493555580T^10 + 169407308640762620085933160597599120T^9 + 698545865865095496350873237321288874T^8 - 1292699670982664072004165953289975552T^7 - 505316963797428638034138121593355512T^6 + 1943998258237962328932351927104831040T^5 + 142849376365152697481163983826326634T^4 - 1559076824193899778858619351522756800T^3 - 52912284260963932942946689331970468T^2 + 820349089697858180287004856848627568T + 284805687406045189533586630147368774.
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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