Specialization at T = 153/172 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -46899334113383125285632T^8 + 270055671557662617610752T^7 - 110499855853494623134464T^6 - 1097978606080292495697408T^5 + 798354426662958846861720T^4 - 652775607268414350434100T^3 - 1472431025874707052625953T^2 + 2703862379229266288830500T - 984764302175595161629827,
A6 = 3885040300642071987577481657671680T^12 - 33785823226478031065590325732302848T^11 + 71535134823792731310067418119643136T^10 + 161716991851894171424472252351774720T^9 - 720321276317174942738930961334015104T^8 - 173535940015248246031810704538019520T^7 + 2662884349300283514864711968426262768T^6 + 18543461312481910222042123064099856T^5 - 4146251221815493809167896322067912459T^4 + 1352969495572413131622726277427086950T^3 + 2682293599935058314574939466346897591T^2 - 2185595594424745389481946472892633500T + 480683366018569365299225874952658046.
It is a 2-neighbour of the fibration given in curve#4205 (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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