{
  "id": 2238,
  "curve_key": "5208320395217569:-375873250739651327171953",
  "ainvs": [
    "1",
    "0",
    "0",
    "-108506674900366",
    "435038475610151312900"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 108.56710145323119,
  "faltings_height": 6.680082853525381,
  "conductor": "4958957190",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "37",
    "53",
    "79",
    "97"
  ],
  "discriminant": "1927307004305578172576828209970971545600",
  "regulator": "3.924441860596583643069825493593708236509",
  "points": [
    [
      "6034076",
      "42923714"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-53, q=44; A=(3q-p)(p+q)^3=-134865, B=-(p+3q)(p-q)^3=72101167. 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 19:49:02",
  "updated_at": "2026-09-26 19:49:02"
}