{
  "id": 2478,
  "curve_key": "94695814161:-24428253654014841",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1972829462",
    "28273934936549"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 75.82180690534842,
  "faltings_height": 4.3164871468244455,
  "conductor": "3652110",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "31"
  ],
  "discriminant": "146079823177194035059161000000",
  "regulator": "5.538606017431691919934157852058505756997",
  "points": [
    [
      "-20211",
      "7749007"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-21, q=10; A=(3q-p)(p+q)^3=-67881, B=-(p+3q)(p-q)^3=268119. 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 20:04:06",
  "updated_at": "2026-09-26 20:04:06"
}