Specialization at T = -709/119 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -70781753951590292657527T^8 - 367565467671631265368148T^7 - 564938152357888095468709T^6 + 861671225097878262924926T^5 + 883290795135789128496595T^4 + 1492235942354111474368304T^3 - 390179707279847183534299T^2 - 1933866828077577012667322T - 753991179760473695494012,
A6 = 7240259042863556427532625579222554T^12 + 56530289701184340202303695554449444T^11 + 163263464615793597915652884274103291T^10 + 33336026591601761367769399981188740T^9 - 608655863176039416519152300146091520T^8 - 922975179177849633814913734492373280T^7 + 1471644379398400596650029609789831050T^6 + 1259508950348326801233446624368517040T^5 - 1608259867492513771432473315149086770T^4 - 1344292356731452517237148523695223300T^3 + 750512254493731351508294582787338435T^2 + 986666108581324895487891684114883660T + 253245346808298629177743261916441680.
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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