{
  "id": 2309,
  "curve_key": "52182514948921:-373776303605365452781",
  "ainvs": [
    "1",
    "0",
    "1",
    "-1087135728103",
    "432611371911566006"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 94.7573057761208,
  "faltings_height": 5.754236389852904,
  "conductor": "2652638070",
  "bad_primes": [
    "2",
    "3",
    "5",
    "19",
    "23",
    "31",
    "61",
    "107"
  ],
  "discriminant": "1380230807215086096924461522468062500",
  "regulator": "5.169213186871413313596942653641559016341",
  "points": [
    [
      "-1132130",
      "461346797"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-38, q=23; A=(3q-p)(p+q)^3=-361125, B=-(p+3q)(p-q)^3=7036411. 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 19:53:34",
  "updated_at": "2026-09-26 19:53:34"
}