{
  "id": 2416,
  "curve_key": "682642676802529:-17835699775531875934033",
  "ainvs": [
    "1",
    "0",
    "0",
    "-14221722433386",
    "20643169851351690660"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 102.47097801419946,
  "faltings_height": 5.923450210208031,
  "conductor": "155645490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "71",
    "73"
  ],
  "discriminant": "37223652121616383577532003225600",
  "regulator": "8.068246102622135123822821536470122017642",
  "points": [
    [
      "2287860",
      "283837830"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-35, q=36; A=(3q-p)(p+q)^3=143, B=-(p+3q)(p-q)^3=26127503. 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 20:00:15",
  "updated_at": "2026-09-26 20:00:15"
}