{
  "id": 2338,
  "curve_key": "20131906499929:-73464954936490493533",
  "ainvs": [
    "1",
    "0",
    "1",
    "-419414718749",
    "85028848077118916"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 91.89998118144312,
  "faltings_height": 5.663531606941494,
  "conductor": "369244590",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "61",
    "83"
  ],
  "discriminant": "1598515307095866683721660829797502500",
  "regulator": "4.238856210815355827190708687651325587645",
  "points": [
    [
      "-553002",
      "384791638"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-50, q=11; A=(3q-p)(p+q)^3=-4923477, B=-(p+3q)(p-q)^3=-3858677. 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 19:55:21",
  "updated_at": "2026-09-26 19:55:21"
}