{
  "id": 3658,
  "curve_key": "548030398068288:-12771187171827889641984",
  "ainvs": [
    "0",
    "0",
    "0",
    "-11417299959756",
    "14781466634060057456"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    4
  ],
  "naive_height": 101.81205561679693,
  "faltings_height": 6.316213414567726,
  "conductor": "194542926481728",
  "bad_primes": [
    "2",
    "3",
    "11",
    "29",
    "67",
    "97",
    "101",
    "1613"
  ],
  "discriminant": "862707017239744704227099870361478889472",
  "regulator": "3236770.8944167730102420023077731152088904277085866",
  "points": [
    [
      "645838",
      "2770762320"
    ],
    [
      "3069115886/1681",
      "10267480088624/68921"
    ],
    [
      "16004444734/19321",
      "6519132594056016/2685619"
    ],
    [
      "347085081022/316969",
      "338232146933316240/178453547"
    ],
    [
      "2892327629038/3996001",
      "20977847411002788240/7988005999"
    ],
    [
      "182039598413587909/291257740489",
      "441515209433797663971483303/157186851160324987"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 13/16 of the Elkies-Klagsbrun Z/4 fibration E1: y^2 + a*xy + a*c*y = x^3 + c*x^2, a = (8t-1)(32t+7), c = 8(t+1)(15t-8)(31t-7) (arXiv:2003.00077, eq. (5)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:28:18",
  "updated_at": "2026-09-29 19:28:18"
}