{
  "id": 4738,
  "curve_key": "0:2743952973192",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-3175871497"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 57.280841375191535,
  "faltings_height": 2.83105935705759,
  "conductor": "12703485987",
  "bad_primes": [
    "3",
    "109",
    "199"
  ],
  "discriminant": "-4357221017991444832563",
  "regulator": "127.3678004371098658330923167140705908563133408",
  "points": [
    [
      "2587",
      "118902"
    ],
    [
      "65073/4",
      "16593611/8"
    ],
    [
      "65073/16",
      "16203145/64"
    ],
    [
      "21691/9",
      "2808971/27"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cube-sum curve x^3 + y^3 = 21691 (Weierstrass model y^2 = x^3 - 432*21691^2). Source: Elkies & Rogers, 'Elliptic Curves x^3+y^3=k of High Rank', ANTS-VI (LNCS 3076, 2004), arXiv:math/0403116, https://arxiv.org/abs/math/0403116.",
  "created_at": "2026-10-20 21:27:25",
  "updated_at": "2026-10-20 21:27:25"
}