{
  "id": 2624,
  "curve_key": "21991388007681:-95878753333079937921",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-458153916827",
    "110970893859173579"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 92.16501611535705,
  "faltings_height": 5.636651249572888,
  "conductor": "100990890",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "59"
  ],
  "discriminant": "834933414809997970354150046784000000",
  "regulator": "14.7068797624722759694616872685821057489413",
  "points": [
    [
      "-718713",
      "263041006"
    ],
    [
      "295083",
      "38211898"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-39, q=20; A=(3q-p)(p+q)^3=-679041, B=-(p+3q)(p-q)^3=4312959. 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 20:13:26",
  "updated_at": "2026-09-26 20:13:26"
}