{
  "id": 2581,
  "curve_key": "143748441:-1723456071261",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-2994759",
    "1995489513"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 56.3507261770966,
  "faltings_height": 2.3251541852555118,
  "conductor": "6930",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11"
  ],
  "discriminant": "35596085895562500",
  "regulator": "2.550393544124009643812867570297125497204",
  "points": [
    [
      "-1833",
      "37299"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-21, q=1; A=(3q-p)(p+q)^3=-192000, B=-(p+3q)(p-q)^3=-191664. 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 20:10:43",
  "updated_at": "2026-09-26 20:10:43"
}