{
  "id": 2179,
  "curve_key": "28336977705340381476720506965067436481:-150844353701180415364853516294381029751466036398967849121",
  "ainvs": [
    "1",
    "0",
    "0",
    "-590353702194591280765010561772238260",
    "174588372339329184400865798305984325852297773091859600"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    8,
    2
  ],
  "naive_height": 258.71169279669226,
  "faltings_height": 19.154324062516665,
  "conductor": "1565117437821917694330",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "67",
    "239",
    "1151",
    "39679",
    "48761"
  ],
  "discriminant": "74837036235453814811572246475871672573324843483088588564423513916440631640375942776949250654233600000000",
  "regulator": "208305.99874409815681806634855818933604505043",
  "points": [
    [
      "4043145978848660830/9",
      "174836140793270820642525880/27"
    ],
    [
      "-344320394143837595000245442992956696/814862753036115169",
      "-434298487065859430358209850792879439798635022311026124/735574559415602783298880303"
    ],
    [
      "1451737788330638657633482779601154870036516263378345751837531961063344239611753112849556760/3155136161424248768625112088369105899244411500618381837275221737203503929",
      "107360513440730689070029083206307720462995748894071425185832190680260396195579613118258628735894896986022984370130847040150217732224660/5604374640684366142548869049661504017759384690908932215403119227589334003883898544252546288500646931113819283"
    ]
  ],
  "submitter": "Tom Fisher",
  "history": [],
  "commentary": "Found by Campbell - Goins (2003). The third independent point was found by M. Watkins (March 2005). ",
  "created_at": "2026-09-26 16:54:54",
  "updated_at": "2026-09-26 16:54:54"
}