{
  "id": 2453,
  "curve_key": "342359313409:-80726493357199873",
  "ainvs": [
    "1",
    "0",
    "0",
    "-7132485696",
    "93432847011840"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 79.6773799394784,
  "faltings_height": 4.69733054265361,
  "conductor": "21411390",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "23",
    "31"
  ],
  "discriminant": "19450887720043700961553947033600",
  "regulator": "3.057902184313398500758570638710523852582",
  "points": [
    [
      "-88116",
      "6188196"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-31, q=8; A=(3q-p)(p+q)^3=-669185, B=-(p+3q)(p-q)^3=-415233. 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 20:02:31",
  "updated_at": "2026-09-26 20:02:31"
}