Specialization at T = 113/64 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -299179532755056721600T^8 + 17595572277256973050240T^7 - 417198241841028433831120T^6 + 1640729978369826838604080T^5 - 3100722994060599052732840T^4 + 3447605855872936235820160T^3 + 2242797006715822622440160T^2 - 6780974649680701579123160T - 3861433387934633535827467,
A6 = 4059456937701100750406882080000T^12 - 282164040891383692833079679552000T^11 + 6335982179671782376102889433278336T^10 - 57358833600342341658935952553773440T^9 + 596470207133623029963843326957746320T^8 - 2651283194034110828378464332085379520T^7 + 3864693449523759808880763001015666800T^6 + 2106280696838105770175445350531933136T^5 - 6473880048439824158203228245177202440T^4 - 4211251865396149188236650636780633280T^3 + 4195370517911125633418237460366830320T^2 + 7286118774738610034794421910368398280T + 2836757717663966250804688091791547974.
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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