{
  "id": 4813,
  "curve_key": "0:-10802413053079776",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "12502792885509"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 73.83709186984925,
  "faltings_height": 4.210746898279067,
  "conductor": "7719497774712813154676004",
  "bad_primes": [
    "2",
    "3",
    "269",
    "1721436443"
  ],
  "discriminant": "-67530166533187689477105682992",
  "regulator": "52644998.735422853943234998090169710087240865055828115489",
  "points": [
    [
      "-20865",
      "1849122"
    ],
    [
      "-12225",
      "3267378"
    ],
    [
      "9043",
      "3638996"
    ],
    [
      "24223",
      "5168726"
    ],
    [
      "961503",
      "942820506"
    ],
    [
      "-92775/4",
      "1282851/8"
    ],
    [
      "-25383/4",
      "27996867/8"
    ],
    [
      "-6375/4",
      "28282851/8"
    ],
    [
      "18897/4",
      "28406457/8"
    ]
  ],
  "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^3-463066403167, giving y^2=x^3+12502792885509. I recovered nine rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [9,9]. Rational torsion trivial. Source-attributed existing curve.",
  "created_at": "2026-10-20 21:46:30",
  "updated_at": "2026-10-20 21:46:30"
}