Specialization at T = 2/1 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -1514324488040382021552T^8 + 54272277189707511223872T^7 - 591511378048151427927072T^6 + 508063749731038184428512T^5 - 136938741575533789662000T^4 - 1349191793967592327593264T^3 + 2932284504423022894260000T^2 + 1053383284052353089252396T - 2783171113600789327601367,
A6 = 44549962755947395534698409178496T^12 - 1693056117252550785873714686294784T^11 + 21575677941893867020743091398042240T^10 - 126989060702986786740910506616083840T^9 + 604500920208636167244898036604209536T^8 + 157197955421771732041959401485834176T^7 - 2431613790180256867483636634863226688T^6 + 80227062221723361472990833995217840T^5 + 4121456489545992568565603195410675236T^4 + 44671471294135497947381190393251640T^3 - 3860959108216677291627323697767945196T^2 - 282581272382058990631068152666505732T + 1744104189782696812246440603003980826.
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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