Specialization at T = 5/2 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -111272277595347481399552T^8 - 571677299335038766946944T^7 - 414437999094511764043024T^6 + 1035179743123152506406800T^5 + 662097824240016643327160T^4 + 815994324653724323045120T^3 - 1173674032798223873117584T^2 - 1437219526913596795113976T - 361162322085565372999627,
A6 = 14017789577932496860029321164394496T^12 + 107552457791941270066673288429907968T^11 + 247298982788864524389713744611492352T^10 - 86954791407743286472040661661146880T^9 - 1006107482862739641862761048136361904T^8 - 241137273409585441201147837083740736T^7 + 2061063776469007784252972194463786352T^6 - 8144469449242082226324505727313744T^5 - 1635536224802875100792289970610279784T^4 - 164213104675413544335944722096034560T^3 + 887798893937215693740812283719232832T^2 + 504859995173227668638395021468280872T + 83905010208748238142485898220128646.
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 ·