Elliptic Curve Rank Leaderboard

Specialization at T = 7/2 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where A4 = -4505943394275807984192T^8 + 52980291620776162887552T^7 - 331691816140954740938736T^6 - 523944665267054297606640T^5 + 845300299497227347100760T^4 - 1642234256419962398088672T^3 + 246946848567560622997776T^2 + 5627761674121177889229000T - 4516338503114727494506875, A6 = 116816047040551151889517539873024T^12 - 2060050809167332071751695581116416T^11 + 18412638495454417247201410610781312T^10 - 40800313765336647939058137401925120T^9 - 11012846950180332303068155006051056T^8 + 1064724795536936542804757035648974528T^7 + 74801504042697709025857109411374608T^6 - 4178046358163385705380531645236403664T^5 + 393751226136259880507039408579785464T^4 + 7329668110287569443800658599168206880T^3 - 1977247101474084220684442672481828000T^2 - 6488561441371188321193822317113175000T + 3856841937412106545376986975288593750. It is a 2-neighbour of the fibration given in curve#4187 (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.