Specialization at T = 50/43 of a rank-17 fibration of X1092 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -906180833179571257456587T^8 - 1930046192084997346024728T^7 + 6011648406192813483229776T^6 + 8355472943604505878941856T^5 - 9649478959250650200991080T^4 + 7450754699414011152778704T^3 - 27984481563110444272430064T^2 - 17758766835719522469182592T - 3317283523979050195432512,
A6 = 332150243825525078123196022294739334T^12 + 1126061667323176712064227845083588744T^11 - 2713185092886283310031062058684874464T^10 - 12015892423153220327930309833774827360T^9 + 7554319779210673373159460328484862840T^8 + 58673243715970603365442249112691953136T^7 - 9754551868147305475783193074338006384T^6 - 149812543158867507723474722158888312896T^5 + 23811683678756345915421047541045697680T^4 + 99714459519208696131901088663865684480T^3 + 64761255203716406202557626472759415936T^2 + 18947601952381150031159658003937314816T + 2277468715827369848274981635668809984.
It is a 2-neighbour of the fibration given in curve#728: 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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