{
  "id": 2603,
  "curve_key": "485645475102529:10327137013452474247967",
  "ainvs": [
    "1",
    "0",
    "0",
    "-10117614064636",
    "-11952705719815609840"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 101.44949999560482,
  "faltings_height": 6.376486439762041,
  "conductor": "1710215130",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "31",
    "53",
    "157"
  ],
  "discriminant": "4566243186188487375650642503023096729600",
  "regulator": "52.7593226214429980003418049410827369080489",
  "points": [
    [
      "-2092516",
      "238165556"
    ],
    [
      "3707918",
      "1227334016"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-1, q=52; A=(3q-p)(p+q)^3=20826207, B=-(p+3q)(p-q)^3=23075935. 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 20:12:08",
  "updated_at": "2026-09-26 20:12:08"
}