{
  "id": 4748,
  "curve_key": "0:1030691601403721518086129246359072348957816356593352200",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-1192930094217270275562649590693370774256731894205269"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 248.73965011253335,
  "faltings_height": 18.78596008516941,
  "conductor": "4771720376869081102250598362773483097026927576821075",
  "bad_primes": [
    "3",
    "5",
    "7",
    "13",
    "19",
    "23",
    "31",
    "43",
    "59",
    "61",
    "73",
    "79",
    "103",
    "109",
    "157",
    "457"
  ],
  "discriminant": "-614771514585745345388702014937083440173787277052610313846784425214738511773064284865564132181269232201875",
  "regulator": "71633425232431364.3461603726033451688129675673690537516273911",
  "points": [
    [
      "23642591593617729121/144",
      "98252123534609206746112660367/1728"
    ],
    [
      "88310759603519640769/64",
      "-829701375518392147007908984353/512"
    ],
    [
      "186947444570606201329/484",
      "2529513158175975931208754740643/10648"
    ],
    [
      "367546341152848996609/324",
      "7043534341799824998039842493011/5832"
    ],
    [
      "6021515587456251202009/676",
      "467259732332479638700440654732135/17576"
    ],
    [
      "8127471096051103790569/64516",
      "465319221889540295783669347447015/16387064"
    ],
    [
      "53988119916600845996329/41616",
      "-12540897742116496657715664117492149/8489664"
    ],
    [
      "66647515276479419963521/592900",
      "6885324121542825089712908509944819/456533000"
    ],
    [
      "119330278066293515680489/692224",
      "36104560562310529545792372775365003/575930368"
    ],
    [
      "206456077678646367560641/1156",
      "-93808352391299389272941929514640813/39304"
    ],
    [
      "610310937232689051741769/3168400",
      "-435183850967477439582792610957898853/5639752000"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cube-sum curve x^3 + y^3 = 13293998056584952174157235 (Weierstrass model y^2 = x^3 - 432*13293998056584952174157235^2). 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 Points mapped from the 3-isogenous curve uv(u+v)=A given there via the dual isogeny.",
  "created_at": "2026-10-20 21:28:04",
  "updated_at": "2026-10-20 21:28:04"
}