Specialization at T = -5/46 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -55167841848013120672432T^8 - 332957956141194498177568T^7 + 30491322260931582308864T^6 + 1529425586966988026755040T^5 - 1952037697734560475124240T^4 + 2598926506840431770721968T^3 - 1867830095998069273733704T^2 - 277424385594374102335720T - 14777266661889408077275,
A6 = 4598281008482828350515082915932544T^12 + 42978899384640031706121578829901184T^11 + 92492192628018200121094722387755072T^10 - 190123782916092378560803318012553920T^9 - 804112508567836069639299650095483056T^8 + 453677299928650241856349297890606048T^7 + 3341413915638233675031424423024721088T^6 - 4626422467332761770277917962033627744T^5 + 1280672988092416347275859838092852864T^4 + 274908311165313855430793313344325200T^3 + 204841690501474358540727164780007400T^2 + 26424146202979804837762201204291000T + 968816204643834101037115185253750.
It is a 2-neighbour of the fibration given in curve#4191 (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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