Specialization at T = -373/1268 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -73932522356183031905227T^8 + 649309903876882877687472T^7 - 1685916835628140824312084T^6 + 645581139407117375333216T^5 - 406054368862523371209330T^4 - 858600221311968331297296T^3 + 1074013049265607843957676T^2 + 189439686366819237655008T - 279637802575984309948587,
A6 = 7677120880090165783883135437481350T^12 - 104661205483741457154365858257793680T^11 + 560585458424820914639770163531974620T^10 - 1380712030244078852090340039520473600T^9 + 959024595422485011830600330788665450T^8 + 2176075475403505129770137846307997920T^7 - 1812178037587130500705886817575824920T^6 - 1469296539009918506803974573439080480T^5 + 1256479376113039680818470745801469450T^4 + 491406111407235947158204600615297520T^3 - 440604154329209614719459225390266084T^2 - 63212663150279697924996150457217184T + 62214320185228162206822083588855334.
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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