{
  "id": 2091,
  "curve_key": "4047764035902908662259856:3402748747421353709134734972745394496",
  "ainvs": [
    "0",
    "0",
    "0",
    "-84328417414643930463747",
    "-3938366605811751978165202514751614"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2
  ],
  "naive_height": 169.98062061185186,
  "faltings_height": 12.221722839773093,
  "conductor": "81988082219777126188462072560",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "31",
    "41",
    "89",
    "107",
    "109",
    "127",
    "131",
    "137",
    "163",
    "337",
    "1279"
  ],
  "discriminant": "31679085932749793358568834548575981499312020110637728162686000000000000",
  "regulator": "35628697642.57981255965173108151241631110098387752269159035",
  "points": [
    [
      "-229660402593",
      "-57579043584503650"
    ],
    [
      "-491335408647/4",
      "-540617810859876875/8"
    ],
    [
      "-5931677762353/121",
      "11738754602704946250/1331"
    ],
    [
      "-4825103885233777/100489",
      "7969579987914151155450/31855013"
    ],
    [
      "-24557881927698/361",
      "264179465546670700600/6859"
    ],
    [
      "-7427793077241822/49729",
      "809237254052456503463750/11089567"
    ],
    [
      "-255949859193",
      "-29633091477508750"
    ],
    [
      "-67128279741697/529",
      "835832830839098467950/12167"
    ],
    [
      "1760582467407",
      "-2303211897512621150"
    ],
    [
      "23284549315535319/9025",
      "-3530065473387776627212622/857375"
    ]
  ],
  "submitter": "Steps Unbounded",
  "history": [],
  "commentary": "2-isogenous partner of curve#1085 (dujella); 4-isogenous partner of curve#1137 (David Renshaw). Isogenous to curve#2023 (also ours).",
  "created_at": "2026-09-26 06:55:10",
  "updated_at": "2026-09-26 06:55:10"
}