{
  "id": 2444,
  "curve_key": "551911437889:51223397514365087",
  "ainvs": [
    "1",
    "0",
    "0",
    "-11498154956",
    "-59287297895280"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 81.10996029523491,
  "faltings_height": 4.826448811048538,
  "conductor": "50907270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "19",
    "31",
    "43",
    "67"
  ],
  "discriminant": "95770734286110045127440151449600",
  "regulator": "7.695519267742468112617454972788586841466",
  "points": [
    [
      "475774",
      "319397650"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-31, q=12; A=(3q-p)(p+q)^3=-459553, B=-(p+3q)(p-q)^3=397535. 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 20:01:59",
  "updated_at": "2026-09-26 20:01:59"
}