{
  "id": 3991,
  "curve_key": "170235172866769065913441:38922140351837527140844424546491375",
  "ainvs": [
    "1",
    "1",
    "1",
    "-3546566101391022206530",
    "-45048773556845244140445824700049"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "naive_height": 160.47440341126583,
  "faltings_height": 11.419138759388508,
  "conductor": "5823102912675542002999614449352786",
  "bad_primes": [
    "2",
    "3",
    "11",
    "19",
    "23",
    "47",
    "97",
    "107",
    "109",
    "271",
    "353",
    "563",
    "1153",
    "1291",
    "5051",
    "9377"
  ],
  "discriminant": "1978289755317522871792254824288020695298141269616499352705717246432",
  "regulator": "863164056985025.77788779825544421733488232095770178005790680580",
  "points": [
    [
      "-891007252471698059/17363889",
      "97729782068624315246859133/72355325463"
    ],
    [
      "-778716859771/16",
      "224232888334709949/64"
    ],
    [
      "-22883730282011/1521",
      "-131366499086420430019/59319"
    ],
    [
      "-20654609951281/1369",
      "-113548950865083680499/50653"
    ],
    [
      "-49776203444859/2401",
      "-520407056893803560321/117649"
    ],
    [
      "570200153981",
      "-428160135259331589"
    ],
    [
      "374684088231",
      "-226334721398978393"
    ],
    [
      "22696445236869/169",
      "95786829866731989907/2197"
    ],
    [
      "62014931434979/169",
      "481664502292446855537/2197"
    ],
    [
      "-2622960703528009/180625",
      "141356030846575417675311/76765625"
    ],
    [
      "-45757347016489/1849",
      "-417413199965872499067/79507"
    ],
    [
      "-5619942358727819/269361",
      "-623074365630163750244807/139798359"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3633 (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 04:40:56",
  "updated_at": "2026-10-05 04:40:56"
}