{
  "id": 5684,
  "curve_key": "0:1165092533584488",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-1348486728686"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 69.38315381348727,
  "faltings_height": 3.839585393582234,
  "conductor": "261851969871589756596804441",
  "bad_primes": [
    "3",
    "568163",
    "9493661"
  ],
  "discriminant": "-785555909614769269790413323",
  "regulator": "7990402683849336.139150776165005457757438862220911038500654",
  "points": [
    [
      "115080635372113/38019556",
      "-1234534883389547806283/234428582296"
    ],
    [
      "220948355788934928267452914153/17216793027704062484272036",
      "62485750114509436806211923965734666698240407/71437852040650417535552239014982448216"
    ],
    [
      "38829760227930867017608882/179420030707195405009",
      "241945846520690469357203663456173469471/2403291165552751623002098021223"
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      "20159101677288098657854369/119804366915248334400",
      "90499314444841130941328061034572103153/1311320868925979148475019328000"
    ],
    [
      "145636484322725958169/1703886408900",
      "1757540249991581746699913089697/2224134046129437000"
    ],
    [
      "13210861524414816462121/297129910862137600",
      "1506743452879342311485246362218581/161964397202486364122624000"
    ],
    [
      "8049380874442333048482049/92660048498000281600",
      "-22813745383288412053320569829458910593/891946457075785252764123136000"
    ],
    [
      "1448597352867771976700689/86740341030243280900",
      "1469601881316548186765170965325268387/807851783195738538469166123000"
    ],
    [
      "260682427614462935020948/10204750074596477401",
      "-127599917541236013208226928240819533/32598946053889760946299594851"
    ],
    [
      "5142070619374137338295712/7498217813803287769",
      "11660203951974263994837650073427312426/20532275264516257396984069603"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Rational 3-isogenous partner of the Burkhardt rank-10 curve y² = x³ + 2330185067168976, arising from parameters (u,v,w) = (1/2,-1,2/3), t = -22/71.",
  "created_at": "2026-10-24 09:03:15",
  "updated_at": "2026-10-24 09:03:15"
}