{
  "id": 2189,
  "curve_key": "11506873874664169:-1228219587951581963316853",
  "ainvs": [
    "1",
    "0",
    "1",
    "-239726539055504",
    "1421550429040823091806"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 110.94516293982957,
  "faltings_height": 7.080956170508526,
  "conductor": "976245270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "29",
    "59"
  ],
  "discriminant": "8727131944514990205038559098939928726758400",
  "regulator": "3.361766905088629266677688425449761398006",
  "points": [
    [
      "9839388",
      "3916070593"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-32, q=59; A=(3q-p)(p+q)^3=4113747, B=-(p+3q)(p-q)^3=109267795. 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 19:45:57",
  "updated_at": "2026-09-26 19:45:57"
}