{
  "id": 68,
  "curve_key": "0:-40586013776330216163919368288",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "46974552981863676115647417"
  ],
  "rank_lower_bound": 15,
  "naive_height": 131.74644205965896,
  "faltings_height": 9.036526080763208,
  "conductor": "238313731807359099208895797698912716157803778347364012",
  "bad_primes": [
    "2",
    "3",
    "1201",
    "6539317",
    "32344001",
    "61641367"
  ],
  "discriminant": "-953254927229436396835583190795650864631215113389456048",
  "regulator": "6004179571973955.9594170979361628807478033739008721205590284254100767",
  "points": [
    [
      "134903368",
      "7030622192107"
    ],
    [
      "192112402",
      "7352882361535"
    ],
    [
      "225027274",
      "7639981722671"
    ],
    [
      "225083527",
      "7640541103540"
    ],
    [
      "258845527",
      "8019816949840"
    ],
    [
      "323938954",
      "8998197347759"
    ],
    [
      "396959044",
      "10465465248949"
    ],
    [
      "493287703",
      "12923142427688"
    ],
    [
      "618875539",
      "16852542091394"
    ],
    [
      "800577328",
      "23666090147563"
    ],
    [
      "832883668",
      "24994838653493"
    ],
    [
      "900602302",
      "27882595405255"
    ],
    [
      "1938425152",
      "85618874611435"
    ],
    [
      "-3801659403949148854700590661/10563498456094496025",
      "20677120321600099128973780340089600900562/34332992588487460476311920125"
    ],
    [
      "-45422308525362180658274681/138657052360580625",
      "177509449917854185325666317221372981128/51631286351368162487765625"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Provenance: Noam D. Elkies, \"j = 0, rank 15; also 3-rank 6 and 7 in real and imaginary quadratic fields\", NMBRTHRY posting, December 30, 2009. This is the Mordell curve y^2 = x^3 + 46974552981863676115647417. The submitted witnesses consist of integral points on this curve plus two points obtained from integral points on the 3-isogenous curve y^2 = x^3 - 27K via the dual 3-isogeny.",
  "created_at": "2026-05-29 11:30:20",
  "updated_at": "2026-07-01 22:41:39"
}