{
  "id": 5465,
  "curve_key": "0:67995796156252704",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-78698838143811"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 77.5164445538884,
  "faltings_height": 4.517359621948996,
  "conductor": "668898769520062210023101201868",
  "bad_primes": [
    "2",
    "3",
    "83",
    "16691",
    "18935929"
  ],
  "discriminant": "-2675595078080248840092404807472",
  "regulator": "501527083903.3791240913188588244792904448879088987087689243",
  "points": [
    [
      "2144017/4",
      "3138566503/8"
    ],
    [
      "83455615/121",
      "762309358898/1331"
    ],
    [
      "262048105/2304",
      "4126996840139/110592"
    ],
    [
      "263038129/4624",
      "3227786264425/314432"
    ],
    [
      "3306483307/7569",
      "190039733117488/658503"
    ],
    [
      "4267351273/69696",
      "225978215075189/18399744"
    ],
    [
      "8299626481/48400",
      "750191270002871/10648000"
    ],
    [
      "40530207607/49729",
      "8158995141169658/11089567"
    ],
    [
      "66136113241/36100",
      "17008077381297539/6859000"
    ],
    [
      "2042118047959/21836929",
      "2774282988269030270/102043969217"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Rank-10 Mordell curve obtained using Mestre's polynomial cube-completion construction from the integer sextuple (-63,-59,-41,49,51,63).",
  "created_at": "2026-10-22 07:10:53",
  "updated_at": "2026-10-22 07:10:53"
}