{
  "id": 2605,
  "curve_key": "650907619168849:-16605599545151586360793",
  "ainvs": [
    "1",
    "0",
    "0",
    "-13560575399351",
    "19219442787951571305"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 102.3281665260866,
  "faltings_height": 6.205347247316591,
  "conductor": "2692356810",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "19",
    "29",
    "67"
  ],
  "discriminant": "17985038618541174603172472435019278400",
  "regulator": "22.7382977447255204841107665925144305378158",
  "points": [
    [
      "8225887/4",
      "1365331613/8"
    ],
    [
      "2146780",
      "39674335"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-29, q=38; A=(3q-p)(p+q)^3=104247, B=-(p+3q)(p-q)^3=25564855. 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 20:12:16",
  "updated_at": "2026-09-26 20:12:16"
}