{
  "id": 4668,
  "curve_key": "0:38763487743264",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-44865147851"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 62.57699976391846,
  "faltings_height": 3.2724058894515,
  "conductor": "72463733700915237055236",
  "bad_primes": [
    "2",
    "3",
    "1433",
    "31308547"
  ],
  "discriminant": "-869564804410982844662832",
  "regulator": "21006193.311662162893888854830655916075318577684953386611",
  "points": [
    [
      "3651",
      "61660"
    ],
    [
      "3695",
      "74718"
    ],
    [
      "4623",
      "232246"
    ],
    [
      "5315",
      "324468"
    ],
    [
      "10563",
      "1064764"
    ],
    [
      "57155",
      "13662468"
    ],
    [
      "28337/4",
      "4459017/8"
    ],
    [
      "36785/4",
      "6848631/8"
    ],
    [
      "67193/16",
      "10936269/64"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Mordell curve y^2 = x^3 - 44865147851, rank exactly 9 (PARI ellrank 2-descent: lower = upper = 9). Found by a Mestre-Nagao sieve over all |k| <= 10^12 (a_p via sextic residue classes for p = 1 mod 3), top candidates certified with ellrank.",
  "created_at": "2026-10-20 19:26:47",
  "updated_at": "2026-10-20 19:26:47"
}