{
  "id": 4743,
  "curve_key": "0:571885697016565128",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-661904741917321"
  ],
  "rank_lower_bound": 6,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 81.77543107186222,
  "faltings_height": 4.87227516511348,
  "conductor": "2647618967669283",
  "bad_primes": [
    "3",
    "73",
    "103",
    "439"
  ],
  "discriminant": "-189266927344978315129990066820403",
  "regulator": "28924832.679234045110111284402075646699867742541409",
  "points": [
    [
      "634666753/5776",
      "11317948775967/438976"
    ],
    [
      "1023719977/484",
      "32753414198001/10648"
    ],
    [
      "1812172537/10404",
      "72150583246111/1061208"
    ],
    [
      "17094269353/179776",
      "-1072077799685397/76225024"
    ],
    [
      "10704126731473/15968016",
      "34982367236825796487/63808191936"
    ],
    [
      "236991605579281/1784217600",
      "3090479185676774967929/75365351424000"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cube-sum curve x^3 + y^3 = 9902523 (Weierstrass model y^2 = x^3 - 432*9902523^2). 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 21:27:45",
  "updated_at": "2026-10-20 21:27:45"
}