{
  "id": 215,
  "curve_key": "2446506415688056704084825:-4479452808061048582945635774140428125",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-50968883660167848001767",
    "5184551861194511414139157441329641"
  ],
  "rank_lower_bound": 18,
  "naive_height": 168.78512849138983,
  "faltings_height": 12.056369141579205,
  "conductor": "5692233049957592618627388003164315988519877481788141693279603950",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "1641821",
    "6169133",
    "19823469628629700195532996237768951332198248209"
  ],
  "discriminant": "-3137843468789122931018347636744329188671582461835713108420381677437500",
  "regulator": "637156633527749476.44719296654871370884618117594544024639322389824847313621",
  "points": [
    [
      "124382151439",
      "27735090940849243"
    ],
    [
      "139856705149",
      "-28138915164057362"
    ],
    [
      "46552881319",
      "53969333884318678"
    ],
    [
      "-208337990336",
      "82222089599352493"
    ],
    [
      "-61208135681",
      "89860755353561878"
    ],
    [
      "51849193319",
      "-51780761335278122"
    ],
    [
      "138959488114",
      "-28021728457973057"
    ],
    [
      "-159455928961",
      "-96215746848427157"
    ],
    [
      "-54052543061",
      "88213549492595743"
    ],
    [
      "913563564151/4",
      "-590980570363245601/8"
    ],
    [
      "120995404208",
      "28087487052518733"
    ],
    [
      "79772580818",
      "40327102621276359"
    ],
    [
      "-168653863876",
      "94781091428093613"
    ],
    [
      "-763198531",
      "-72273444214523922"
    ],
    [
      "-981027959149/4",
      "-433225119414961251/8"
    ],
    [
      "14219450798539",
      "53612964608312831743"
    ],
    [
      "5762465089339/36",
      "7252249875034931683/216"
    ],
    [
      "1114322441480",
      "-1154149212334190531"
    ]
  ],
  "submitter": "RoyManami",
  "commentary": "Rank-18 naive-height record: h=168.785 (beats prior r18 height record 173.853). Found via Mestre/Fermigier quartic family, sextuple mestre_ais(u=-6,v=-4), specialization T=962; certified by hyperellratpoints + Neron-Tate height-pairing independence (18 independent points).",
  "created_at": "2026-06-25 20:55:28",
  "updated_at": "2026-07-01 22:31:42"
}