Specialization at T = -11/115 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -1294316468457527272747T^8 - 61482963914543295234088T^7 - 943435684374763790645824T^6 - 2688743270213054211837664T^5 - 3856670928366631764978280T^4 - 999902363213138391166096T^3 + 2961913384000561526356496T^2 + 1046903749166543421058688T - 943686476906321498328832,
A6 = 32662063813788609918746258888614T^12 + 1796450107115792990741776388684984T^11 + 35062265377401817193324124680756816T^10 + 316874613294458685885325494699025760T^9 + 1878352364777031985219759926555560760T^8 + 3544464889310281997809284624918208080T^7 + 1303911666228891105042353858020750800T^6 - 1471880942788787576791593483327263040T^5 + 252670343673375657835921804367034960T^4 + 730639334234102885410704041977318400T^3 - 1097948334966447155670068911813786880T^2 - 383111400250142557306211553242163200T + 375132589068583102936074200430223360.
It is a 2-neighbour of the fibration given in curve#4187 (itself a 2-neighbour of the fibration 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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