{
  "id": 2502,
  "curve_key": "53522452729:-12382279921201933",
  "ainvs": [
    "1",
    "0",
    "1",
    "-1115051099",
    "14331249580466"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 74.11010123995833,
  "faltings_height": 3.7974425215319636,
  "conductor": "1009470",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "23"
  ],
  "discriminant": "1386485606500090126222500",
  "regulator": "5.003094890605409025925515292147476054526",
  "points": [
    [
      "-53685/4",
      "41529731/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-22, q=1; A=(3q-p)(p+q)^3=-231525, B=-(p+3q)(p-q)^3=-231173. 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 20:05:35",
  "updated_at": "2026-09-26 20:05:35"
}