Specialization at T = -660/137 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -485042948797679528112T^8 + 12463578805199058894528T^7 - 230629938307243679610144T^6 - 1586012147509225586376096T^5 - 3868907398105357015696080T^4 - 6794745991541079206248224T^3 - 4791118686138149116505904T^2 + 6061871481875161826582772T - 1374235222299991775805627,
A6 = 3820001086939854414872700973440T^12 - 155249980524531925200471635032320T^11 + 5279785372691676756614905714258560T^10 + 22439305421110286908829252745667200T^9 + 198311921848923368813090766393603840T^8 + 1955108933617356512048828761030033920T^7 + 6903605561322701279549833535328289920T^6 + 8139034537986456490540355512081445520T^5 - 1317692978359257302156310289643874060T^4 - 2476393922218195353910049397638432280T^3 + 5841882186136964852470754649206854356T^2 - 3899452237007593054578752344925650716T + 735364979113660346489805816953176854.
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.
apkorte ·