{
  "id": 4006,
  "curve_key": "210819649823495432226171898273723201:-40324293109388156847546111485561829149672418257396449",
  "ainvs": [
    "1",
    "0",
    "0",
    "-4392076037989488171378581214035900",
    "46671635543273329318653514757313287975016864406032"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 244.0089332898237,
  "faltings_height": 18.390824814260984,
  "conductor": "216095858582728308893742177217643607485136038653170",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "29",
    "31",
    "37",
    "67",
    "79",
    "139",
    "157",
    "211",
    "241",
    "257",
    "509",
    "709",
    "2801",
    "12301",
    "16529",
    "50263",
    "53617"
  ],
  "discriminant": "4481374339012390278609292200373604626354568421949817199606571622276114685170561160216601825865463360000",
  "regulator": "57628563213127232063.194151972195750545818795269632274534739956704290",
  "points": [
    [
      "-66693294685778516",
      "6553028237693922154776928"
    ],
    [
      "1837243956133593448/169",
      "-1004446946908920825989789180/2197"
    ],
    [
      "4728043801450864",
      "-5100137277981833025024692"
    ],
    [
      "47333700900215092048/10201",
      "-5292965201746106204810891866444/1030301"
    ],
    [
      "-388198946675292026456/57121",
      "-119176367177471066913678306902068/13651919"
    ],
    [
      "206559596378800276507/676",
      "-2900532392118782705489403461557/17576"
    ],
    [
      "5545962403792712527024/11881",
      "408926574987127995382677133628692/1295029"
    ],
    [
      "4638847445058061786/9",
      "9909926135245940546202587696/27"
    ],
    [
      "2158682621705379592002691/3319684",
      "3155390786859440142168870830737059109/6048464248"
    ],
    [
      "-193015984748414647741514/8720209",
      "297020515159760173037565122487839296/25750777177"
    ],
    [
      "-252672162148169174792108/26224641",
      "1260487931641043180667556270626011188/134296386561"
    ],
    [
      "978718824189990343432/114921",
      "122482816347500229066140008802012/38958219"
    ],
    [
      "2801669911452742227693568/8532241",
      "-4596138085025071715926257058444688164/24922675961"
    ],
    [
      "441378011219593127766080239/7283939716",
      "1082235383926119634349655899207889282653/621655119001736"
    ],
    [
      "57679337162506514938567664776/14389681849",
      "13850682743126322951420236376528205790861444/1726143065560493"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3650 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 15: 15 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 04:44:17",
  "updated_at": "2026-10-05 04:44:17"
}