Specialization at T = 153/79 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -46118133600050365068267T^8 - 175585131457438249904328T^7 + 186310120046915943350856T^6 + 1086331850638516901792016T^5 - 496083140846252073481680T^4 + 514411161151166512216704T^3 - 1349221054433071325320224T^2 - 2378315976590397135297312T - 727839380732795443417392,
A6 = 3720542197990934008634945538033126T^12 + 21526619776657745210072107363777176T^11 + 8750301169726091012404314376074744T^10 - 195259865254986340553776941743082000T^9 - 376011441894779917411915234538303040T^8 + 641327438884246873021760128611712704T^7 + 2168837359823326715713321889328303264T^6 - 1791411665482428423973793516575869984T^5 - 3162380047574807481299569084055523120T^4 + 550294990071515361307367747441559360T^3 + 2282676589946398330859127503834660544T^2 + 1241084125645116952889139651480184704T + 235518724223176451772618983340821376.
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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