{
  "id": 2229,
  "curve_key": "4302212249437921:-282174637005809315171281",
  "ainvs": [
    "1",
    "0",
    "0",
    "-89629421863290",
    "326591007583901552100"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 107.99371728577786,
  "faltings_height": 6.671075824689622,
  "conductor": "4020008190",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "37",
    "107",
    "181"
  ],
  "discriminant": "4196094329748306610904822448390144000000",
  "regulator": "2.312304455785677762136226839585883378143",
  "points": [
    [
      "5428470",
      "87267360"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-37, q=48; A=(3q-p)(p+q)^3=240911, B=-(p+3q)(p-q)^3=65711375. 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 19:48:28",
  "updated_at": "2026-09-26 19:48:28"
}