{
  "id": 90,
  "curve_key": "50382476556585671117196535329:-10477821508261035890454685894244764009751217",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1049634928262201481608261153",
    "12127108227154239133795359409449990039537"
  ],
  "rank_lower_bound": 19,
  "naive_height": 198.26832281426988,
  "faltings_height": 14.48079488427077,
  "conductor": "1751718228241340476861580569821746434717712624403433485131514999870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "19",
    "37",
    "8574497",
    "181208356857259",
    "4413293403451386737",
    "4037539076961879275231"
  ],
  "discriminant": "10477910772405735373306877059383665173459657501610235009100067004657607156983398400",
  "regulator": "10371257585479461054.35598398694932580359550898384903385812428978701472381867",
  "points": [
    [
      "-8779463831497",
      "143755449342791785188"
    ],
    [
      "24240245774135",
      "30446890111192735716"
    ],
    [
      "-22245461900617",
      "156423538644219166308"
    ],
    [
      "36555310855883",
      "-150352607095203320592"
    ],
    [
      "-8080699457113",
      "141708301267997242020"
    ],
    [
      "-14846294273337",
      "156326553803804543268"
    ],
    [
      "36476994847767",
      "149582124592754048612"
    ],
    [
      "-34924411096447",
      "78658644953248301238"
    ],
    [
      "59607687170287/9",
      "-1996141721696772632564/27"
    ],
    [
      "-26267158673455",
      "146883134785122482568"
    ],
    [
      "-16834995329497",
      "-158197280846105092812"
    ],
    [
      "342081548339663",
      "6299474080859475015468"
    ],
    [
      "14189440889847",
      "9501613201130832932"
    ],
    [
      "-20800327426857",
      "-157988981093285571132"
    ],
    [
      "526338098596415",
      "12052885365530882707908"
    ],
    [
      "9835031446475",
      "-52490357206977923004"
    ],
    [
      "-37100686104889",
      "-1280640675347457756"
    ],
    [
      "-36314897406925",
      "-48512158639169211804"
    ],
    [
      "109946355750407/49",
      "33926203667374622610684/343"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "New curve of rank >= 19 and naive height 198.268, found as the specialization T = 3251/8 (t = 3251/16) 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 an exhaustive minimal-height scan crossed with a staged Nagao-sum sieve; 19 independent points certified by positive-definite Neron-Tate height pairing.",
  "created_at": "2026-06-11 18:51:20",
  "updated_at": "2026-07-01 22:30:42"
}