{
  "id": 2656,
  "curve_key": "854240576809:-766249203060031573",
  "ainvs": [
    "1",
    "0",
    "1",
    "-17796678684",
    "886861020485146"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 82.42043609078603,
  "faltings_height": 4.782534629546007,
  "conductor": "570570",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19"
  ],
  "discriminant": "20963275841017002738621185409600",
  "regulator": "5.00170973675726011649343038055202521505192",
  "points": [
    [
      "-152452",
      "7611198"
    ],
    [
      "-142762",
      "22829343"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-8, q=19; A=(3q-p)(p+q)^3=86515, B=-(p+3q)(p-q)^3=964467. 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 20:15:57",
  "updated_at": "2026-09-26 20:15:57"
}