{
  "id": 1136,
  "curve_key": "-5691897724251230907058950270704:-3439314899788457993844900435152012413789358656",
  "ainvs": [
    "0",
    "1",
    "0",
    "118581202588567310563728130640",
    "3980688541421865908832460581640572647559008"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "naive_height": 212.44978950466503,
  "faltings_height": 15.777252008327586,
  "conductor": "1128310354841987032068083640",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "23",
    "31",
    "41",
    "53",
    "61",
    "67",
    "109",
    "257",
    "263",
    "6857"
  ],
  "discriminant": "-113560926037211684803407333113505047703110088238583058026856495778931997572812500000000000",
  "regulator": "59790824866.3121062410180920959660139748198208762753845",
  "points": [
    [
      "5214659183189899/9",
      "441349788112072855468750/27"
    ],
    [
      "91631075910969091/81",
      "29030385893943634923511250/729"
    ],
    [
      "905996088091705279/1089",
      "-936064675494166647788897500/35937"
    ],
    [
      "181695539961568031611701181/401213295396",
      "3118285747119114456193015291293289398125/254134118289961944"
    ],
    [
      "358208889629899/9",
      "-79928149832769347821250/27"
    ],
    [
      "458511607229899/9",
      "-86036943515434214421250/27"
    ],
    [
      "107350398144202730260261/55860676",
      "-35742600898558708737841355227370625/417502692424"
    ],
    [
      "104311761791152531/225",
      "-42503582484330078229795754/3375"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Obtained by computing a rational isogeny from curve#1108 and mapping all 8 independent witness points to the global minimal model. Isogenies preserve the Mordell-Weil rank; the image points are independently certified by the site verifier. Torsion computed exactly with PARI/GP elltors. Conductor is unchanged by the isogeny.",
  "created_at": "2026-09-23 21:37:11",
  "updated_at": "2026-09-23 21:37:11"
}