{
  "id": 1815,
  "curve_key": "5483584448571734401:-11932207832855864058328359649",
  "ainvs": [
    "1",
    "0",
    "0",
    "-114241342678577800",
    "13810425722951952992443007"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    4,
    2
  ],
  "naive_height": 129.4448719724388,
  "faltings_height": 8.743636108687488,
  "conductor": "4465971815216415",
  "bad_primes": [
    "3",
    "5",
    "7",
    "17",
    "19",
    "23",
    "31",
    "37",
    "73",
    "101",
    "677"
  ],
  "discriminant": "13027862718945297163189740607223655147886782013100625",
  "regulator": "947.341737215444130779239251998016450213487562919",
  "points": [
    [
      "-268943626",
      "5008331048693"
    ],
    [
      "-29540491",
      "4142404520903"
    ],
    [
      "-47051669987/144",
      "6966846517291535/1728"
    ],
    [
      "9124880681/25",
      "569215966744264/125"
    ],
    [
      "13209530054/25",
      "1255980319774873/125"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Found by a smooth-support search in the universal family y^2=x(x+u^2)(x+v^2) with (u,v)=(18445,49932), motivated by reverse-engineering the arithmetic pattern in Eroshkin's Z/2Z x Z/4Z examples. The listed global minimal model has PARI/GP 2.17.4 rank bounds [5,5], torsion Z/2Z x Z/4Z, conductor 4465971815216415 and minimal discriminant 13027862718945297163189740607223655147886782013100625. The five listed rational points are independent; their canonical-height pairing determinant is approximately 947.3417372154. Against the snapshot of 2026-09-25, this improves the rank-5 Z/2Z x Z/4Z conductor by a factor of about 892.41 and the absolute discriminant by about 4.22e22.",
  "created_at": "2026-09-25 15:15:12",
  "updated_at": "2026-09-25 15:15:12"
}