Specialization at T = 15/29 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -24011570250321173399907T^8 - 356625422779304362612668T^7 - 1671152276752436694790849T^6 - 1732924520270453003282874T^5 - 1590147679200142298997105T^4 + 386386685489195171580024T^3 + 1390900315063766269994001T^2 - 109185086941693427240802T - 395834418180372108310812,
A6 = 1216216238839692796812141066344094T^12 + 26209873296759406934598983518866084T^11 + 230543686141973991553199370733886191T^10 + 1052224609079923489090821191968978740T^9 + 2393956796589717261918365468578783320T^8 + 629549415237804682066795998544524480T^7 - 1844893995718784103700959635524244430T^6 - 226188479515226331041573622292694160T^5 + 1278208881685740455186312823654525570T^4 + 13862357385931867527612871612710300T^3 - 504285816967908504474275294387026905T^2 + 26689064927161462765535195704544220T + 94664857047267576565599696553129920.
It is a 2-neighbour of the fibration given in curve#4205 (itself a 2-neighbour of the fibration 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 ·