{
  "id": 3963,
  "curve_key": "22020238582542551629297936:-99175554668438701269320001215157621184",
  "ainvs": [
    "0",
    "1",
    "0",
    "-458754970469636492277040",
    "114786521606836319256741604057154900"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2,
    2
  ],
  "naive_height": 175.06201259371238,
  "faltings_height": 12.517439097368596,
  "conductor": "536728523406795140805407760",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "31",
    "59",
    "101",
    "149",
    "199",
    "389",
    "1301",
    "3001",
    "24439"
  ],
  "discriminant": "487050243034594509266852843153263051024593865379213165727764505600000000",
  "regulator": "6045593265705.4607040584935732819992930564924799325807951",
  "points": [
    [
      "11623873831860519888770/15999973081",
      "-821948000821724102313788496000000/2023852594988771"
    ],
    [
      "1249013211822905/2704",
      "-5330318119437843494325/140608"
    ],
    [
      "335356926212617970/323761",
      "-159639574821887141426649600/184220009"
    ],
    [
      "2253102218368862591105/4436625664",
      "-33414763471469157058303849365825/295514762227712"
    ],
    [
      "11340369117581986505/8479744",
      "33975274682565829589920769925/24693014528"
    ],
    [
      "18833195780511705009911971/36009756660969",
      "-28922104189208289987985487024974121380/216087815897979367797"
    ],
    [
      "3301642414588534226/4068289",
      "4318667323126368863997991680/8205738913"
    ],
    [
      "974096670159694568857596770/1902295179165481",
      "-9866933536136664546019801125405338400000/82969192048512815948629"
    ],
    [
      "6408657376201715638419266/1560113412025",
      "16015283258065986844911795899920740864/1948651856722766125"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3673 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 9: 9 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.",
  "created_at": "2026-10-05 04:35:21",
  "updated_at": "2026-10-05 04:35:21"
}