{
  "id": 4814,
  "curve_key": "0:-1323545004933214464",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "1531880792746776"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 83.45369084096535,
  "faltings_height": 5.012130145872074,
  "conductor": "28971095841808529447047634496",
  "bad_primes": [
    "2",
    "3",
    "2969",
    "7417",
    "322057"
  ],
  "discriminant": "-1013756585696564062411090826284032",
  "regulator": "162664234901.7079242171886635346598925790683589371342415175",
  "points": [
    [
      "8574",
      "39147300"
    ],
    [
      "5554590",
      "13091214924"
    ],
    [
      "-52592767175/538756",
      "9699551213581421/395446904"
    ],
    [
      "-264063/16",
      "2501233857/64"
    ],
    [
      "-249734/25",
      "4890814064/125"
    ],
    [
      "46063194/625",
      "686827519128/15625"
    ],
    [
      "85080426/25",
      "784789028424/125"
    ],
    [
      "173991534/7225",
      "24145710883452/614125"
    ],
    [
      "913080174/10201",
      "48860734093020/1030301"
    ],
    [
      "222092051854650/222875041",
      "3312344041301135531736/3327301487089"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Tom Womack's 2003 thesis, Explicit Descent on Elliptic Curves, Table 3.3: https://johncremona.github.io/theses/womack.pdf. This is the rational 3-isogenous partner of the Mordell curve y^2=x^3-56736325657288, giving y^2=x^3+1531880792746776. I recovered ten rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [10,10]. Rational torsion trivial. Source-attributed existing curve.",
  "created_at": "2026-10-20 21:47:56",
  "updated_at": "2026-10-20 21:47:56"
}