{
  "id": 2597,
  "curve_key": "2715511743591201:-141497760431824332426801",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-56573161324817",
    "163770570198642567809"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 106.61327045413685,
  "faltings_height": 6.566483164663216,
  "conductor": "669278610",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23"
  ],
  "discriminant": "1492090506978762325517397463044096000000",
  "regulator": "4.06870503472669441685528915501148229494623",
  "points": [
    [
      "4298007",
      "121189876"
    ],
    [
      "4309767",
      "56321716"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-51, q=40; A=(3q-p)(p+q)^3=-227601, B=-(p+3q)(p-q)^3=51996399. 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 20:11:46",
  "updated_at": "2026-09-26 20:11:46"
}