{
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  ],
  "submitter": "Matthias Breddin",
  "history": [],
  "commentary": "Exact rank 18, unconditional: rational 2-torsion point, 18 independent points (Neron-Tate height matrix of rank 18; the archived certificate additionally saturates the lattice at all primes up to 97 — the points listed here are the ellrank output, not the saturated basis) with matching 2-descent upper bound 18 (PARI/GP 2.15.4 ellrank, effort 3). Fiber t=-4087/15630 on branch u=29/13 of the Elkies-Klagsbrun Z/2Z rank-9 family (arXiv:2003.00077), found by a Mestre-Nagao residue-table sieve followed by an exact 2-descent-type upper bound and ellrank (Matthias Breddin, 2026-09-02; method: doi:10.5281/zenodo.22242107).",
  "created_at": "2026-09-02 13:41:25",
  "updated_at": "2026-09-02 13:41:25"
}