{
  "id": 4862,
  "curve_key": "0:-118089683454351047983380540000",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "136677874368461861091875625"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    3
  ],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 133.88248375180615,
  "faltings_height": 9.214529555108808,
  "conductor": "65605379696861693324100300",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "23",
    "31",
    "83",
    "4201"
  ],
  "discriminant": "-8070123459692610914690549350424656171231508362668750000",
  "regulator": "4280187.47996822128327285560703616355610776315172481174",
  "points": [
    [
      "248610979",
      "12330607336442"
    ],
    [
      "259337650",
      "12414503280025"
    ],
    [
      "823711075",
      "26373581199350"
    ],
    [
      "58174969086",
      "14031509431198959"
    ],
    [
      "-39439286271/400",
      "93198915410978817/8000"
    ],
    [
      "24612486921/64",
      "7123124452293531/512"
    ],
    [
      "44718594750/289",
      "58210804449583425/4913"
    ],
    [
      "1016602720650/529",
      "1034829899129894175/12167"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Elkies and Rogers (2004), Elliptic Curves x^3+y^3=k of High Rank: https://arxiv.org/abs/math/0403116. This is the rational 3-isogenous partner of the cube-sum curve with k=23381862574950. I recovered eight rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [8,8]. Rational torsion Z/3Z. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:12:52",
  "updated_at": "2026-10-20 22:12:52"
}