{
  "id": 2282,
  "curve_key": "2572041329490361:-130441763021757411028141",
  "ainvs": [
    "1",
    "0",
    "1",
    "-53584194364383",
    "150974258291314139806"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 106.45042881049694,
  "faltings_height": 6.42700427886329,
  "conductor": "821230410",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "23",
    "29",
    "41"
  ],
  "discriminant": "11532121383332454203746625726610562500",
  "regulator": "4.843681238688760274893633671189387972007",
  "points": [
    [
      "4223585",
      "-296928"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-46, q=41; A=(3q-p)(p+q)^3=-21125, B=-(p+3q)(p-q)^3=50704731. 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 19:51:50",
  "updated_at": "2026-09-26 19:51:50"
}