Specialization at T = 1249/283 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -25474223654459729695152T^8 + 93424157542535492313792T^7 + 249549530991798533589216T^6 - 697407234931421362933344T^5 - 624235669206688152877680T^4 - 597548430366277034810016T^3 - 3503195429735821784150304T^2 + 3443481263994739372563948T - 932157668798019061834527,
A6 = 1558176592694379366370572668882304T^12 - 8556444096428535116807109681029376T^11 - 10909694949700311770505743225764224T^10 + 132365209573836556400929013899470720T^9 - 65939622169833360804191934552439680T^8 - 921173694379955547822888188003154432T^7 + 724370040233725908757397970764697408T^6 + 3685802165670854989077288042679139952T^5 - 921815011359411216952545051496976700T^4 - 3541405794655636698734958615621659160T^3 + 4046594122834363561792364624080217124T^2 - 1844492709789748579332256815007671156T + 328955182757185562525000064586958946.
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 ·