Specialization at T = 399/62 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -2315727727754537200T^8 - 385085454700810899360T^7 - 21602016129394505916480T^6 + 522753273151467123362400T^5 - 5286101242963131414221040T^4 + 36372271295130380430902640T^3 - 119866073107198500927623880T^2 - 44611766420397375005288280T - 17644996097302241306504187,
A6 = 1527906580671423711878454400T^12 + 405036291873933234226307839360T^11 + 29619810420503480598512683442496T^10 + 83447431068127636496045716863680T^9 + 10401708370692526999699168797492240T^8 - 680407910276562698898410450598391200T^7 + 10353906760921511571152027566046979840T^6 - 64341197016007520540432295631610298720T^5 + 151935569584040641348413346807219047840T^4 - 98223779992621049253987068203224001200T^3 + 461589258984786807406908653536129872360T^2 + 245414512415050160861358750620214278280T + 41992607521879070487127955356093746390.
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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