{
  "id": 2809,
  "curve_key": "5438541672116096770201009531983311281:-18586326255791921414651708427387387727733071085314969321",
  "ainvs": [
    "1",
    "0",
    "0",
    "-113302951502418682712521031916318985",
    "21511951684944353479738305462052364088462449985347225"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    10
  ],
  "naive_height": 254.5240423690122,
  "faltings_height": 19.237701785554545,
  "conductor": "207378196450271490213570",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "23",
    "29",
    "37",
    "83",
    "179",
    "421",
    "449",
    "5861"
  ],
  "discriminant": "-106823944732617416030358799767323582173740988672258596991452999865830259836585006945609995130535550668800000",
  "regulator": "230938.4247833852103331831290591961805227989981",
  "points": [
    [
      "78814203761183644250/169",
      "581683965894328314177329774255/2197"
    ],
    [
      "3436332008458468416478730/34210801",
      "21124025259460851169358866870250108395/200098975049"
    ],
    [
      "1398754563943005473930/5329",
      "38620446628503258559292776320155/389017"
    ],
    [
      "11640543532109526978519663626/690060361",
      "1255666719143271256369948583563017883103663/18127195623109"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1887 via the rational 2-torsion point x=203769462231968570. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny.",
  "created_at": "2026-09-26 20:23:25",
  "updated_at": "2026-09-26 20:23:25"
}