{
  "id": 86,
  "curve_key": "2536381595032617889:166595742322888303250363663",
  "ainvs": [
    "1",
    "0",
    "0",
    "-52841283229846206",
    "-192819150610486916434364"
  ],
  "rank_lower_bound": 15,
  "naive_height": 127.13181051112655,
  "faltings_height": 8.662454551552132,
  "conductor": "75863584261726271948809574125392066219010",
  "bad_primes": [
    "2",
    "5",
    "7",
    "19",
    "896405796700345079",
    "63632217828750709343"
  ],
  "discriminant": "9426722265250752028761189313525609860226811622809600",
  "regulator": "791888638835.30221384169538421040548888858303566962292163142474760247",
  "points": [
    [
      "-86289844",
      "1929897590322"
    ],
    [
      "232261116",
      "252042240242"
    ],
    [
      "-19704724",
      "-916915922718"
    ],
    [
      "-219385604",
      "-916819471118"
    ],
    [
      "-226833604",
      "-349143487278"
    ],
    [
      "-223779924",
      "652546002082"
    ],
    [
      "-63014844",
      "1699073084522"
    ],
    [
      "-49541412",
      "1517727177010"
    ],
    [
      "649349116",
      "15468856647442"
    ],
    [
      "-224413004",
      "-603000225518"
    ],
    [
      "-4649124",
      "-229662735118"
    ],
    [
      "-15204004",
      "-779136381518"
    ],
    [
      "-85738692",
      "-1925430491150"
    ],
    [
      "-121604004",
      "-2105804614478"
    ],
    [
      "-133371844",
      "2117209895922"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "New curve of rank >= 15 and naive height 127.13, found as the specialization T = 1043/2 (t = 1043/4) of the 2-parameter Mestre rank-12 family over Q(t) used by Fermigier in 'Une courbe elliptique definie sur Q de rang >= 22' (Acta Arith. 82 (1997), sextuple {0,55,314,378,1007,1036}), located by a staged Nagao-sum sieve over ~1.9M specializations; 15 independent points certified by positive-definite Neron-Tate height pairing.",
  "created_at": "2026-06-11 15:29:48",
  "updated_at": "2026-07-01 22:41:38"
}