{
  "id": 3993,
  "curve_key": "123992060531547759561:-12636395921898099689443401383685",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-2583167927740578324",
    "14625458243583407363235377664"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "naive_height": 143.22826801024155,
  "faltings_height": 9.993455526508672,
  "conductor": "2521187658201578085610417610020422",
  "bad_primes": [
    "2",
    "3",
    "17",
    "31",
    "61",
    "73",
    "109",
    "139",
    "151",
    "307",
    "349",
    "499",
    "1237",
    "1637",
    "3301"
  ],
  "discriminant": "-91303382004233281769658736489447812533563219971277027953648",
  "regulator": "1219567982656528980.4487046649563902644378045864663287657490531",
  "points": [
    [
      "-8924235840440203270204208/3494881525655529",
      "13969766734839534592286167126364157400/206608738975215825734667"
    ],
    [
      "-1809480509764373252735/650782637521",
      "9274897564468370931599644243668/524993512297203431"
    ],
    [
      "5944988358231585145/3576398809",
      "26128757286663440197225287369/213879377974627"
    ],
    [
      "1359675005543365840/3208429449",
      "21199079193183436666658533016/181735069279707"
    ],
    [
      "5303412166341514615044025/736328684932129",
      "12148009865482978402976878435239923139/19980556461547539827633"
    ],
    [
      "-19511509993062829757900/8147194040241",
      "1956222263364099732583166661847412/23254772217687053289"
    ],
    [
      "152372785354712807199097/62542205339769",
      "74672165000498429000939958283358420/494606462647431588147"
    ],
    [
      "4187962152359250806478865/1300478446249609",
      "9344664683496033010885474573221400321/46898044898984998450523"
    ],
    [
      "1312539149876888503936305/51148715259889",
      "1501419811035693775375909374470628219/365807069703277726537"
    ],
    [
      "4241556759317619307010177521/1113413157785763025",
      "287944784545346061076189195104252183122859/1174855688247288893554633625"
    ],
    [
      "-3049266202452143892455247180/1858739367325758241",
      "304604892905630262590293194605991621008148/2534123322039366433681894961"
    ],
    [
      "2655767856513108516675367613652/758420835212741453809",
      "4600575925841793153854333446364331398009584296/20886486183526129055522610621623"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3630 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 12: 12 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 04:41:27",
  "updated_at": "2026-10-05 04:41:27"
}