Specialization at T = 239/750 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -32332676430258071809200T^8 - 392497065814316713973280T^7 - 1605286506697565663751840T^6 - 2016536429413138685637600T^5 - 1643121380463324517697040T^4 + 604907641354957338809520T^3 + 2182672220879703769538760T^2 + 284764930480378808601480T - 903774960127741440937707,
A6 = 2152872548702497670524683858518400T^12 + 37926485183963444897543405698016640T^11 + 273497207298763591399877065140889536T^10 + 1038319980551223501714889156644738240T^9 + 2025026435470961119972063737624451920T^8 + 768757757929830231396275004132348000T^7 - 1622968189285827532493125262292017760T^6 - 620910140516148584947737138229395360T^5 + 1602335569642802776124896462486427520T^4 + 351810003192753644435857685852379600T^3 - 1085870391509042811982855754241980040T^2 - 186927270560088531571177963463660760T + 323553892643757904650299161814986470.
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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