{
  "id": 2456,
  "curve_key": "266671933609:1239209608792427",
  "ainvs": [
    "1",
    "0",
    "1",
    "-5555665284",
    "-1434733352654"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 78.92785508035479,
  "faltings_height": 4.645556749297624,
  "conductor": "31141110",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "61"
  ],
  "discriminant": "10973698471681467170217417248400",
  "regulator": "3.780404100927617800955324363550489997307",
  "points": [
    [
      "-295813/4",
      "18129999/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-28, q=11; A=(3q-p)(p+q)^3=-299693, B=-(p+3q)(p-q)^3=296595. 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 20:02:42",
  "updated_at": "2026-09-26 20:02:42"
}