{
  "id": 4714,
  "curve_key": "0:-51753487922136",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "59899870280"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    3
  ],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 63.1550258905287,
  "faltings_height": 3.320574733335687,
  "conductor": "6469185990267",
  "bad_primes": [
    "3",
    "7",
    "11",
    "13",
    "163"
  ],
  "discriminant": "-1550013606543215756249307",
  "regulator": "1054.02292792385768321559174816730302651267447338",
  "points": [
    [
      "-3912",
      "5623"
    ],
    [
      "-1452",
      "238408"
    ],
    [
      "133497/4",
      "48815399/8"
    ],
    [
      "279708",
      "147930568"
    ],
    [
      "326326",
      "186413727"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Elkies and Rogers (2004), Elliptic Curves x^3+y^3=k of High Rank: https://arxiv.org/abs/math/0403116. This is the rational 3-isogenous partner of the cube-sum curve with k=489489. I recovered five rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [5,5]. Rational torsion Z/3Z. Source-attributed existing curve.",
  "created_at": "2026-10-20 21:21:12",
  "updated_at": "2026-10-20 21:21:12"
}