{
  "id": 4815,
  "curve_key": "0:1598282638899665184",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-1849864165393131"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 83.83092275199495,
  "faltings_height": 5.043566138457874,
  "conductor": "168987527427438277691643554724",
  "bad_primes": [
    "2",
    "3",
    "11777",
    "5817567089"
  ],
  "discriminant": "-1478302889935230053246497816725552",
  "regulator": "19795853848.69297509207398796361927247318402954320385841222",
  "points": [
    [
      "169635",
      "55059588"
    ],
    [
      "227635",
      "99727912"
    ],
    [
      "7454883",
      "20354492484"
    ],
    [
      "1640455/9",
      "1751018374/27"
    ],
    [
      "1831627/9",
      "2190044872/27"
    ],
    [
      "10317819/25",
      "32703271128/125"
    ],
    [
      "17695609/144",
      "4176392525/1728"
    ],
    [
      "71330065/484",
      "391392887399/10648"
    ],
    [
      "101621617/484",
      "916353777367/10648"
    ],
    [
      "49417435515/24649",
      "10984251096875916/3869893"
    ]
  ],
  "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+68513487607153, giving y^2=x^3-1849864165393131. 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 21:49:01",
  "updated_at": "2026-10-20 21:49:01"
}