{
  "id": 2539,
  "curve_key": "638993881:12232576695779",
  "ainvs": [
    "1",
    "0",
    "1",
    "-13312373",
    "-14159184244"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 60.82621630918835,
  "faltings_height": 3.087029640415187,
  "conductor": "115710",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "19",
    "29"
  ],
  "discriminant": "64394497051541618062500",
  "regulator": "3.868811340938319353936765781894238395790",
  "points": [
    [
      "-1195",
      "7152"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-14, q=5; A=(3q-p)(p+q)^3=-21141, B=-(p+3q)(p-q)^3=6859. 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 20:07:54",
  "updated_at": "2026-09-26 20:07:54"
}