Specialization at T = -11584/4313 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -154503213541262535600T^8 + 4159635009352858651680T^7 - 21187086453270000393696T^6 - 687438318305734637863392T^5 - 4576470188855512350897360T^4 - 19322004287067422371639920T^3 - 39029689014386535692132184T^2 + 4186478995367154403195512T - 1679949255743694529867467,
A6 = 747141710909816776767093360000T^12 - 29305404314392232038648503024000T^11 + 301598848438544320323778700280000T^10 + 2292679730804159433657382244285760T^9 - 4484131884783219751251582549192624T^8 + 544733850758018343321283421195576736T^7 + 7256453148985237089497289163544883552T^6 + 31881087967205708307154627785355135968T^5 + 53417637701365905114499013007709555776T^4 + 36362990355034819792007607408188452080T^3 + 65566855132366254216911881386291117144T^2 - 854195394262226327944905852404523432T + 424114741036883895390965869842474630.
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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