{
  "id": 4745,
  "curve_key": "0:16523021609796654080737408800",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-19123867603931312593446075"
  ],
  "rank_lower_bound": 8,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 129.9491043367376,
  "faltings_height": 8.886747937186428,
  "conductor": "76495470415725250373784300",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "29",
    "41",
    "47",
    "59"
  ],
  "discriminant": "-157992038841323619249698570739866368205346979015230000",
  "regulator": "2145812661.93237672769405123774575293469121536119078234",
  "points": [
    [
      "269938579",
      "738716913908"
    ],
    [
      "283984639",
      "1943892930862"
    ],
    [
      "644782051",
      "15777843090976"
    ],
    [
      "1679172499",
      "68669534486132"
    ],
    [
      "1502372041/4",
      "-46552218884261/8"
    ],
    [
      "2186568211",
      "102152018376316"
    ],
    [
      "5468797489/4",
      "402908772015287/8"
    ],
    [
      "1196456469121/144",
      "1308694006383930431/1728"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cube-sum curve x^3 + y^3 = 1683200989470 (Weierstrass model y^2 = x^3 - 432*1683200989470^2). 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 21:27:53",
  "updated_at": "2026-10-20 21:27:53"
}