{
  "id": 2288,
  "curve_key": "742094612240689:-20215478806558297014313",
  "ainvs": [
    "1",
    "0",
    "0",
    "-15460304421681",
    "23397543626639327145"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 102.72149358217678,
  "faltings_height": 6.1916641223865705,
  "conductor": "6847602090",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "19",
    "23",
    "29",
    "31",
    "83"
  ],
  "discriminant": "5321081871017800627308552763553793600",
  "regulator": "5.304960212779292506264564141908337446690",
  "points": [
    [
      "2641884",
      "994861161"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-31, q=38; A=(3q-p)(p+q)^3=49735, B=-(p+3q)(p-q)^3=27266247. 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 19:52:15",
  "updated_at": "2026-09-26 19:52:15"
}