{
  "id": 2543,
  "curve_key": "439502121:-3529195690581",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-9156294",
    "4087006308"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 59.703459303049286,
  "faltings_height": 3.033949728431613,
  "conductor": "10710",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17"
  ],
  "discriminant": "41921259685871942250000",
  "regulator": "3.123974337434075463478246872713198794198",
  "points": [
    [
      "-3143",
      "44114"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-12, q=5; A=(3q-p)(p+q)^3=-9261, B=-(p+3q)(p-q)^3=14739. 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 20:08:09",
  "updated_at": "2026-09-26 20:08:09"
}