Specialization at T = 8/11 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -48409603383664787003467T^8 - 394068766077940965499368T^7 - 868178038487744679634824T^6 + 75232746619435737072176T^5 - 1595443198591218244734480T^4 + 2109751284798891015753984T^3 + 698088862800109333591616T^2 - 451094270783465286539232T - 253592240870068502573232,
A6 = 4040236832859543331678148357555974T^12 + 49819909994079550561071236517492344T^11 + 234267578460325937004132088864988136T^10 + 398279879863645004081067873151110480T^9 - 481849875819898361648289850645703040T^8 - 2228123003432291609437160968553906112T^7 + 1566656402007985551644615301279128448T^6 + 1326858671203210206487814863820521632T^5 - 86078958551730838909970610055003440T^4 - 798762607809093749675638617207229120T^3 - 133072535405990991623348292517512896T^2 + 130627123922202571126617921344467584T + 49036442300194391139017017822237056.
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 ·