{
  "id": 2188,
  "curve_key": "20294842506817921:-2890097882612194634441281",
  "ainvs": [
    "1",
    "0",
    "0",
    "-422809218892040",
    "3345020662233716289600"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 112.64742955492568,
  "faltings_height": 7.126740601003221,
  "conductor": "72508206030",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "19",
    "41",
    "101",
    "139"
  ],
  "discriminant": "3696061696198034282181940839262157376000000",
  "regulator": "3.858166166920637946245239915664994678965",
  "points": [
    [
      "12334072",
      "2530659256"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-41, q=60; A=(3q-p)(p+q)^3=1515839, B=-(p+3q)(p-q)^3=143211839. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.",
  "created_at": "2026-09-26 19:45:53",
  "updated_at": "2026-09-26 19:45:53"
}