Specialization at T = -1174/561 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -2543951687432473887460672377483T^8 - 24818956579468052738105064515028T^7 - 77370351271537068433100341247904T^6 - 67467015005869076752518330881556T^5 + 17016806163007175905444072313970T^4 + 82892666432004286839667115406660T^3 + 60326950313063858115906668276136T^2 - 19915299958127111246160446427612T - 27289787224140550157486254128927,
A6 = 1550015425870788606577153334191333100109899718T^12 + 22628758087381124339269406905403241577644202332T^11 + 129666144682594016426381124339897213302125685892T^10 + 345383914891725536644308394433318665228830332532T^9 + 290839421645428584216690391576246831863346739238T^8 - 501824346857271485681078887124327532393736266360T^7 - 846300710982340207425925322969763595750992960552T^6 + 305997138248518386594529888488269900783383863000T^5 + 830499992755676217073833197525717220681011885394T^4 - 107750490807943398511372493107734289465806190692T^3 - 406158893855534218232938145420042389062774860796T^2 + 16099138820538211319454876432431072682872064564T + 80603603306668130852282428774716725293282315746.
It is a 2-neighbour of another fibration built here: 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 ·