Specialization at T = -1790/379 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -48393752778478434415347T^8 + 234108952651394609784372T^7 - 80814256417092311126712T^6 - 679388493916744317276048T^5 + 849130008583102656447600T^4 - 1612877972465689819445088T^3 - 1721372370991450068420576T^2 + 3195581161738120242427584T - 1022262851511189811019952,
A6 = 4288640503583697356313758651467086T^12 - 31081375829532514009215543683973804T^11 + 28276823001661393553469125282330460T^10 + 256926134808356645699750469379877640T^9 - 449617863421297320058465556298389964T^8 - 1048634128416718070202997112516438256T^7 + 2065736410495836489928705601739523680T^6 + 2236546605261081463863864681224077632T^5 - 3826369071427309561101765341099280384T^4 - 533037124876780800676744763435971200T^3 + 3060828262346510699070310919653538688T^2 - 1792851678299100321486790706293201152T + 349240517064527681543842990887408000.
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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