{
  "id": 2187,
  "curve_key": "12861955024848601:-1454522242906236467007901",
  "ainvs": [
    "1",
    "0",
    "1",
    "-267957396351013",
    "1683474795848731400156"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 111.27915037761271,
  "faltings_height": 7.086465003531528,
  "conductor": "28145072670",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "31",
    "59",
    "211"
  ],
  "discriminant": "7012044003652514964329057886794071289062500",
  "regulator": "7.358372126849506114616492007390163092531",
  "points": [
    [
      "10222650",
      "3535138987"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-34, q=59; A=(3q-p)(p+q)^3=3296875, B=-(p+3q)(p-q)^3=115023051. 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 19:45:48",
  "updated_at": "2026-09-26 19:45:48"
}