{
  "id": 2617,
  "curve_key": "138828087931681:-1635601402568309263921",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2892251831910",
    "1893056937877520100"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 97.69277251844663,
  "faltings_height": 5.832977426323438,
  "conductor": "454799730",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "47",
    "59",
    "71"
  ],
  "discriminant": "274786769420095092485436707904000000",
  "regulator": "9.29500133133385534929737317865868410080258",
  "points": [
    [
      "-1808100",
      "1101563610"
    ],
    [
      "-1523508",
      "1663063626"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-59, q=4; A=(3q-p)(p+q)^3=-11812625, B=-(p+3q)(p-q)^3=-11752209. 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 20:13:01",
  "updated_at": "2026-09-26 20:13:01"
}