{
  "id": 2620,
  "curve_key": "38670953356561:-225474692981714056441",
  "ainvs": [
    "1",
    "0",
    "0",
    "-805644861595",
    "260966012702875025"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 93.85832962467502,
  "faltings_height": 5.7718612601858625,
  "conductor": "913628310",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "23",
    "43",
    "53",
    "83"
  ],
  "discriminant": "4045923120658926747505914539289000000",
  "regulator": "21.1059350162896757335243160098069985511514",
  "points": [
    [
      "-891910",
      "520072205"
    ],
    [
      "-837970",
      "590041865"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-53, q=10; A=(3q-p)(p+q)^3=-6599081, B=-(p+3q)(p-q)^3=-5751081. 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 20:13:12",
  "updated_at": "2026-09-26 20:13:12"
}