Specialization at T = 191/42 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -135905733791177100879168T^8 + 1170105215005157329310976T^7 - 3263768771352480615865392T^6 + 2346518634849035692218000T^5 + 245936114819649867667320T^4 - 1432517413140009535585824T^3 + 956236108008185762686704T^2 + 156236369911740531083592T - 257526183060059049073467,
A6 = 20737642716792465943326120257995008T^12 - 244496554556977289037909247323669504T^11 + 1157988470380485097232050906009638528T^10 - 2790680074288331258566479141986856192T^9 + 3101966268250480126177717673389002384T^8 + 656755301509986568870676405232297792T^7 - 3435411333307752838327381281470537136T^6 + 658445704499369672945800020331508016T^5 + 1474214217968126497120054729756719768T^4 - 229935451360122136801662723346458528T^3 - 405994673197848668282333146509853248T^2 + 15664520646757240102474163329610664T + 58525848665960980471096021479565974.
It is a 2-neighbour of the fibration given in curve#4187 (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.
apkorte ·