{
  "id": 2239,
  "curve_key": "778854575242681:19097010433925636234579",
  "ainvs": [
    "1",
    "0",
    "1",
    "-16226136984223",
    "-22103022687740160994"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 102.86653638912169,
  "faltings_height": 6.555798195360061,
  "conductor": "9045810510",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "53",
    "163",
    "167"
  ],
  "discriminant": "62366106360942503694120801918421557562500",
  "regulator": "7.503928483007609609556159187846323227725",
  "points": [
    [
      "-2917823",
      "634334528"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-2, q=55; A=(3q-p)(p+q)^3=24862459, B=-(p+3q)(p-q)^3=30186459. 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 19:49:05",
  "updated_at": "2026-09-26 19:49:05"
}