{
  "id": 4094,
  "curve_key": "-80207:-219309065",
  "ainvs": [
    "1",
    "1",
    "1",
    "1671",
    "254526"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    4
  ],
  "naive_height": 38.411985097206234,
  "faltings_height": 1.2603423199740822,
  "conductor": "1980381",
  "bad_primes": [
    "3",
    "13",
    "17",
    "29",
    "103"
  ],
  "discriminant": "-28132205256831",
  "regulator": "52.672594072313438181557931550109437557563802",
  "points": [
    [
      "-30",
      "437"
    ],
    [
      "9",
      "515"
    ],
    [
      "201",
      "2859"
    ]
  ],
  "submitter": "NDElkies",
  "history": [],
  "commentary": "Smallest naïve height of all curves with this MW group.  This is [a,b,a*b,0,0] with (a,b)=(13,103).  Curves 2-10 are at (a,b) = (24,481/4) [curve#1159], (33,111) [curve#4091], (39,129), (21,127), (3,211) [curve#4092], (19,-89) [curve#4093], (15,155), (11,181), (15,-145).",
  "created_at": "2026-10-09 14:34:43",
  "updated_at": "2026-10-09 14:34:43"
}