{
  "id": 4747,
  "curve_key": "0:109471933998568698819633193562370439200",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-126703627313158216226427307363854675"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 175.1774631073474,
  "faltings_height": 12.655777834737243,
  "conductor": "506814509252632864905709229455418700",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "23",
    "31",
    "37",
    "43",
    "83",
    "109",
    "151",
    "421"
  ],
  "discriminant": "-6935245563302651263483549978476274664745938495668130773655811392361630000",
  "regulator": "38376357796748.64469403093719142970103873967896154480080125",
  "points": [
    [
      "3528379374409/4",
      "5984763094833906277/8"
    ],
    [
      "6110958239731/9",
      "11655021356694595396/27"
    ],
    [
      "10497983708011",
      "34012226270126447216"
    ],
    [
      "83919846442489/36",
      "764916625222063960787/216"
    ],
    [
      "198185567469961/36",
      "2788965029861620279109/216"
    ],
    [
      "315390907055911/289",
      "-5321096238055550334866/4913"
    ],
    [
      "249889953577441/484",
      "1112982603584253549839/10648"
    ],
    [
      "8774707419959359/1225",
      "821815055330484805887898/42875"
    ],
    [
      "10442897018676361/2916",
      "-1065691846252244332562491/157464"
    ],
    [
      "5384554912082001511/3214849",
      "12325049054083396213643921734/5764224257"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cube-sum curve x^3 + y^3 = 137006962414679910 (Weierstrass model y^2 = x^3 - 432*137006962414679910^2). 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 21:28:01",
  "updated_at": "2026-10-20 21:28:01"
}