{
  "id": 1639,
  "curve_key": "-20084625299203938305279:7686860705241494160449442422171519",
  "ainvs": [
    "1",
    "0",
    "0",
    "418429693733415381360",
    "-8896829519920563914931292262400"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    8
  ],
  "naive_height": 156.0496410763687,
  "faltings_height": 11.075931239289638,
  "conductor": "503432816707590",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "31",
    "41",
    "181",
    "809",
    "1171"
  ],
  "discriminant": "-38882990829482360019296008558230635514530722089683179263900000000",
  "regulator": "19240.05977850422291365365073213621429980659887",
  "points": [
    [
      "1219162970880",
      "1346333040895714560"
    ],
    [
      "8816227363050/529",
      "20013000614814336180/12167"
    ],
    [
      "13100620448012280/39601",
      "1502148659724794665320840/7880599"
    ],
    [
      "3206628715676144635689705/44629133694016",
      "5903687567195335801148190481499502465/298145106159408664064"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/8. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-25 02:09:19",
  "updated_at": "2026-09-25 02:09:19"
}