Specialization at T = -3/41 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -77688200046122639977675T^8 - 345051545551894951495160T^7 - 26575925672984725510240T^6 + 1397379174658735482223200T^5 + 924444105192629673167160T^4 - 552617251497682425745200T^3 - 3294538182497011117811760T^2 - 2836363778933196694377600T - 685235941086191704065792,
A6 = 8343511083085250123050296186761350T^12 + 55798071641305709411620408773693480T^11 + 63992696069821126283929842778614576T^10 - 287548516348103372029428932872522080T^9 - 549777946830148798846989863404282920T^8 + 702321721822785932402284527824455920T^7 + 1394771712241954046774251387009862160T^6 - 1833587512252380081925577530665112512T^5 - 1898687314820271014676246427139553840T^4 + 2184401546825882198833306353761222400T^3 + 3375300416127856002328341391809073920T^2 + 1517503055739234059908068559049779200T + 234697979821554858808091582382514176.
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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