{
  "id": 2670,
  "curve_key": "10626488374489:-34640540213909485213",
  "ainvs": [
    "1",
    "0",
    "1",
    "-221385174469",
    "40093199391408476"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 89.9831127096998,
  "faltings_height": 4.938179964306614,
  "conductor": "69233010",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "41",
    "43"
  ],
  "discriminant": "3186965986392926320902188100",
  "regulator": "22.1122141281074136827431163256862502668465",
  "points": [
    [
      "-364511",
      "269177828"
    ],
    [
      "77271",
      "153088492"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-22, q=21; A=(3q-p)(p+q)^3=-85, B=-(p+3q)(p-q)^3=3259787. 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 20:16:56",
  "updated_at": "2026-09-26 20:16:56"
}