Rank ≥ 17. This curve is the specialization at T = 2454 of the Mestre/Fermigier family y² = r(x,T), where r is the degree-≤4 remainder in p₆(x−T)·p₆(x+T) = g(x)² − r (g monic of degree 6), with p₆(x) = ∏ᵢ(x−aᵢ) on the sextuple (a) = (−1146, −2304, −654, 3054, 2880, −1830). It was found by Alexey Pozdnyakov via a Mestre–Nagao sieve of this family for small-conductor, high-rank specializations. The rank lower bound is witnessed by the 17 listed independent rational points, whose 17×17 Néron–Tate height-pairing matrix is positive-definite; the conductor N = 2·5·11·13·10541939988843133587887·5626250600098076816239435529 is by Tate's algorithm. Proven lower bound on the Mordell–Weil rank (no exact-rank, Selmer, or BSD claim). Curve and search by Alexey Pozdnyakov.
Edgar Costa · 2026-06-25 02:06:54
Rank >= 17 witness for the prepared Mestre u4 v6, T=2454 curve from ec_high_rank_search_report.pdf. The first 16 points are from rank16_basis.json; P17=(168529858382/49,65428320462144828/343) was recovered by the Claude point-finding subagent and independently verified here. Sage verified all 17 points lie on the minimal model and that the height-pairing matrix has rank 17.
EDIT: This curve was generated by Alexey Pozdnyakov
Edgar Costa · 2026-06-25 00:14:13
Rank >= 17 witness for the prepared Mestre u4 v6, T=2454 curve from ec_high_rank_search_report.pdf. The first 16 points are from rank16_basis.json; P17=(168529858382/49,65428320462144828/343) was recovered by the Claude point-finding subagent and independently verified here. Sage verified all 17 points lie on the minimal model and that the height-pairing matrix has rank 17.
Edgar Costa · 2026-06-25 21:31:45
Edgar Costa · 2026-06-25 02:06:54
Edgar Costa · 2026-06-25 00:14:13