{
  "id": 4746,
  "curve_key": "0:710520016412543703296998228768800",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-822361130107110767704859061075"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 151.2870998185048,
  "faltings_height": 10.664914227333695,
  "conductor": "1096481506809481023606478748100",
  "bad_primes": [
    "2",
    "3",
    "5",
    "37",
    "41",
    "53",
    "73",
    "1231",
    "4831"
  ],
  "discriminant": "-292152021830371165222660402571504965191696593532757210627230000",
  "regulator": "2674487998201.6181363932607282119952336824943925291401021",
  "points": [
    [
      "11019158827671/49",
      "36576905616998197506/343"
    ],
    [
      "47820873392121/4900",
      "-112287697349482469331/343000"
    ],
    [
      "37257970820479/2601",
      "193001002946826505858/132651"
    ],
    [
      "350304584915631/1369",
      "-6556288770459356143446/50653"
    ],
    [
      "420506348004489/1444",
      "8622865328068735172037/54872"
    ],
    [
      "4637037899528481/183184",
      "307654190121945532796721/78402752"
    ],
    [
      "98802203484786969/620944",
      "31053146583013744704153597/489303872"
    ],
    [
      "22377124010073241/1299600",
      "-3065936107754222340057539/1481544000"
    ],
    [
      "193664403326466091/16641",
      "85226509708085730338154136/2146689"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cube-sum curve x^3 + y^3 = 349043376293530 (Weierstrass model y^2 = x^3 - 432*349043376293530^2). 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 21:27:57",
  "updated_at": "2026-10-20 21:27:57"
}