Specialization at T = -186/163 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -32314259208676675198192T^8 - 220263400022708733054624T^7 - 255006976139783552896608T^6 + 705363094453509328737024T^5 + 1047835198424784109021200T^4 + 1820453244371835449110416T^3 - 1245666920662047666014424T^2 - 3926333297851033484227032T - 1657966129723797525563067,
A6 = 2220158269397315819350729045585024T^12 + 23424072793928593017661886421060992T^11 + 69989708296427149663267141905289920T^10 - 61968539237944624284964605273911360T^9 - 599227600313137750772024638621900656T^8 - 203890468677123352982190860910686112T^7 + 2258581157822950043811972713225053920T^6 + 559769644036858048987416888208533696T^5 - 3908030961820075418207725091990624736T^4 - 1985850721280648599946097200370542160T^3 + 2921751862616849299905524795576315928T^2 + 3089933922534003123866046309582827784T + 831153037936820603440551361962407190.
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.
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