{
  "id": 1084,
  "curve_key": "3918464135366794062479873265191156862541776:-7756643191856580805199011532848695608654393243970903368248502976",
  "ainvs": [
    "0",
    "0",
    "0",
    "-81634669486808209634997359691482434636287",
    "8977596286871042598609967051908212510016658847188545565102434"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2,
    2
  ],
  "naive_height": 294.2228210417262,
  "faltings_height": 21.832250159875063,
  "conductor": "1544209591355171508263116235415332449383972946440",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "23",
    "43",
    "47",
    "53",
    "73",
    "89",
    "317",
    "1319",
    "1367",
    "1987",
    "1993",
    "2281",
    "6221",
    "27481",
    "303313"
  ],
  "discriminant": "77409501948973198317001430574073989940536486795252492314829388942204317042488280067788467662745710255329075360000",
  "regulator": "177779721425.2079650924217424226082612559965607737352473745",
  "points": [
    [
      "162602604340593389143",
      "52300762410704501849143965760"
    ],
    [
      "164984045926475906973",
      "551453736181936832009844750"
    ],
    [
      "177206175739093403913",
      "275793617262026874422316858030"
    ],
    [
      "59549881090154691261345/361",
      "172239516266057855707454174358/6859"
    ],
    [
      "570799616133545344084563/1681",
      "311361373951990006927406672901553200/68921"
    ],
    [
      "235910342109329286050597637/1408969",
      "92329942750540720684149475377216473850/1672446203"
    ],
    [
      "98893595621003375953999596013/599809081",
      "27491994190905203182010605436285044691950/14689924202771"
    ],
    [
      "17464066381308599452453449508143/105923560681",
      "65195101402811059705833869660020343138904960/34473776135677579"
    ],
    [
      "1077650388206334070181148679539213/6532834395481",
      "35707587231014782691169328456223563026174450/16697539277620102621"
    ],
    [
      "786880074494543742402474810528170517/4770143712015529",
      "334925833269966785717105157297989208425995559850/329455828436687153439083"
    ]
  ],
  "submitter": "C. R. Hill",
  "history": [],
  "commentary": "Found with Rank Hunter v0.8.10; family=DMT Triad Family - CEF; parameter=-463/191; local status: rigorous rank lower bound >= 10.",
  "created_at": "2026-09-23 17:15:18",
  "updated_at": "2026-09-23 17:15:18"
}