{
  "id": 1137,
  "curve_key": "17772888756942793400976:-126444516363751253539268415919852224",
  "ainvs": [
    "0",
    "0",
    "0",
    "-370268515769641529187",
    "146347819865452839744523629536866"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2
  ],
  "naive_height": 161.65022334987054,
  "faltings_height": 11.528575659213148,
  "conductor": "81988082219777126188462072560",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "31",
    "41",
    "89",
    "107",
    "109",
    "127",
    "131",
    "137",
    "163",
    "337",
    "1279"
  ],
  "discriminant": "-9249190796881710214856831497600002318742226857585765207325958144000",
  "regulator": "35628697642.57981255965173108151241631110098387752269159035",
  "points": [
    [
      "850458130097",
      "784187466256529280"
    ],
    [
      "146152966257",
      "56693563271115520"
    ],
    [
      "32251357922",
      "12959645450812830"
    ],
    [
      "38151629762",
      "13702297515202890"
    ],
    [
      "12677776497",
      "11987130052613120"
    ],
    [
      "-333477283383/16",
      "770691585902048635/64"
    ],
    [
      "994545732973290393/243049",
      "991819858363919293950693760/119823157"
    ],
    [
      "-13164907518",
      "12204126246933670"
    ],
    [
      "-19757334467647/529",
      "126489491575017056640/12167"
    ],
    [
      "-42557395279",
      "9221086030423680"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Obtained by computing a rational isogeny from curve#1085 and mapping all 10 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 21:37:14",
  "updated_at": "2026-09-23 21:37:14"
}