{
  "id": 4812,
  "curve_key": "0:4325434215302016",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-5006289601044"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 72.0065778537135,
  "faltings_height": 4.058204063601087,
  "conductor": "309418957648411020813456",
  "bad_primes": [
    "2",
    "3",
    "11467",
    "4042429"
  ],
  "discriminant": "-10827188166033198440304452352",
  "regulator": "26650123.806211842904276372018244435732258417918066543615",
  "points": [
    [
      "19942",
      "1710062"
    ],
    [
      "21117",
      "2100087"
    ],
    [
      "24622",
      "3149702"
    ],
    [
      "26230",
      "3611134"
    ],
    [
      "29902",
      "4661542"
    ],
    [
      "33510",
      "5711634"
    ],
    [
      "69753/4",
      "4356531/8"
    ],
    [
      "286990/9",
      "141378382/27"
    ],
    [
      "1724614/25",
      "2247506362/125"
    ]
  ],
  "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+185418133372, giving y^2=x^3-5006289601044. 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 21:45:02",
  "updated_at": "2026-10-20 21:45:02"
}