Specialization at T = 54/103 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -213546515196627504820332T^8 + 869465515207593907398960T^7 - 510065089965030971860884T^6 - 1270257582515056045578720T^5 + 1426065508735989008931900T^4 - 690890144029437273227280T^3 - 1389292332816820391566956T^2 + 1307996517837724132656960T - 286267614586960854758400,
A6 = 38855172470975738993518813988244756T^12 - 243637332934783116837818686074203520T^11 + 382613702852074064448992630465758608T^10 + 438404888400781537256687728554749760T^9 - 1340270054837389026155362835012033304T^8 - 438466811942831565597983911599431040T^7 + 1981768199902501016022471226901183040T^6 + 697917175039489822346233336938891840T^5 - 1626320407404938608434545478196300764T^4 - 187748176254897658526766053163492480T^3 + 919892555571017546557734659258394000T^2 - 417938005135807422838969764298752000T + 59851413200989840657350337781760000.
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.
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