Specialization at T = -250/51 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -15108348426986418946992T^8 - 165645727401183163968960T^7 - 386516497356749936802240T^6 + 804907699137855510269760T^5 - 423101056239642087896040T^4 + 2012740403434408357952040T^3 - 832891923170874739577340T^2 - 2371900038780270082074480T - 881248331824987560372900,
A6 = 717503217218577271350459150984576T^12 + 11638864686052244686069138775512320T^11 + 58135061140664436934300824832212480T^10 + 62512031622436328327919258342862080T^9 - 268895690113423321891997914072476960T^8 - 870815838806588886732350721838471968T^7 + 2170770437820474859902147687346459920T^6 + 114853264658855014380401497670938080T^5 - 2228934495975748087928517866419014780T^4 - 844990471869666800949969469071688800T^3 + 1481780271644919349838123819347167336T^2 + 1307631772289943212553000319429645920T + 318018311456252316549507444881168100.
It is a 2-neighbour of another fibration built here: 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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