Specialization at T = -63/2 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -11858511001583521804032T^8 + 214175721852502381272960T^7 - 1432812052406818812164400T^6 + 1877396101235517581961840T^5 - 1616349363784284403162440T^4 + 375398756942628652907040T^3 + 1483849947541484408156640T^2 - 499683202991392785978600T - 424387235571887878825275,
A6 = 508635860698696309787313618886656T^12 - 13266381990941392781192177963243520T^11 + 139080387761026008655151155338259200T^10 - 731079762012883508969321984907406080T^9 + 2344562178683608195181185875640917840T^8 - 1913494729584525923388480523171587648T^7 - 1946649819060578533441792459632712560T^6 + 2240017571252714640177648881635252560T^5 + 1187496071063136453053032076443570200T^4 - 1140089711639607323530481433639140640T^3 - 523526754044213182839802197400957584T^2 + 245269758021262210799450076829606200T + 113368132470196897298368287244953750.
It is a 2-neighbour of the fibration given in curve#4647: 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 ·