Specialization at T = -5938/5319 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -4437370829345071269937785502500T^8 + 24731294533954602783634178920800T^7 - 24905343694917325040325875752236T^6 - 73371957550294374341624859203376T^5 + 11388134363003403434011617130260T^4 - 31974960227112637988116696606080T^3 - 53087557802286047432098781752884T^2 + 33902036804480905040632762295376T - 4900264269756058995659292474432,
A6 = 3583088599917473486225042501788936057800562500T^12 - 29952862178447015859986519449513030145545410000T^11 + 74261855654700672409867052055125389734923941200T^10 + 34915854636953526118546131005709436129082490240T^9 - 320350491450370659682737733420310606418445799256T^8 + 104052954099599046113301816294931102834227932832T^7 + 846552244341643086726187489356042742190493998112T^6 + 378044570078449717959306675143150641014761409024T^5 - 387170892915283488485440730375460569591982158796T^4 - 122143831120324014405241873122119111177801883600T^3 + 159312688808409642522129729739582813691214920688T^2 - 45075775528724488962464647393974897773506063488T + 4205873318402097235409142015354269085411308544.
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 ·