{
  "id": 85,
  "curve_key": "590444989494967182401424:-153953492867090210501562993326615232",
  "ainvs": [
    "0",
    "0",
    "0",
    "-12300937281145149633363",
    "178186913040613669561994205239138"
  ],
  "rank_lower_bound": 17,
  "naive_height": 164.2054902749314,
  "faltings_height": 11.74463527677641,
  "conductor": "1482227606068422543624563099019961426673156424163925520",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "29",
    "43",
    "379",
    "683",
    "77184794499853885577",
    "395346588657568538203"
  ],
  "discriminant": "105406467094579591296588247874235886027076144817990449651642497766400",
  "regulator": "1817695003829779.04293109872927351022456096418502780356708712404856098214",
  "points": [
    [
      "12769374094",
      "4815991895126940"
    ],
    [
      "125820594673",
      "24946324639382916"
    ],
    [
      "-103323838141",
      "18603782679944990"
    ],
    [
      "-26083877519",
      "21938468531054724"
    ],
    [
      "-11082842866",
      "17696185154606860"
    ],
    [
      "13821257509",
      "3288271100958360"
    ],
    [
      "10629645547",
      "6973761305127870"
    ],
    [
      "105648047179",
      "-7603198829438850"
    ],
    [
      "-109627526642",
      "14463170264818836"
    ],
    [
      "14233545121",
      "2446343252265924"
    ],
    [
      "157251351019",
      "-46177454812786110"
    ],
    [
      "-22414544291",
      "21039141738696840"
    ],
    [
      "-22992476591",
      "-21186336664692540"
    ],
    [
      "-46119352946",
      "-25444106607377700"
    ],
    [
      "197214452197",
      "73638526067350200"
    ],
    [
      "3422924509",
      "-11667126369923640"
    ],
    [
      "315386379763",
      "-166342028869106046"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "New curve of rank >= 17 and naive height 164.205, found as the specialization T = 533 (i.e. t = 533/2) 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), roots {0,55,314,378,1007,1036}), located by a staged Nagao-sum sieve over ~1.9M specializations and certified by Neron-Tate height pairing.",
  "created_at": "2026-06-11 15:11:12",
  "updated_at": "2026-07-01 22:35:40"
}