{
  "id": 4117,
  "curve_key": "8375376673:-334686404622545",
  "ainvs": [
    "1",
    "1",
    "1",
    "-174487014",
    "387295820946"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    4
  ],
  "naive_height": 68.54568566858026,
  "faltings_height": 3.7676355556157493,
  "conductor": "543416329599",
  "bad_primes": [
    "3",
    "11",
    "13",
    "17",
    "37",
    "101",
    "127",
    "157"
  ],
  "discriminant": "275168986539125259851015889",
  "regulator": "5016.41997726863319950311363982733237844220774661",
  "points": [
    [
      "1815",
      "275832"
    ],
    [
      "1875411/25",
      "-2534070374/125"
    ],
    [
      "-10810",
      "-999798"
    ],
    [
      "215387",
      "-99882450"
    ],
    [
      "14219",
      "-891030"
    ]
  ],
  "submitter": "NDElkies",
  "history": [],
  "commentary": "Smallest naïve height H of the 5 curves with H < 2^100 and this MW group.   This curve is [a,b,a*b,0,0] with (a,b)=(127, -15857).  Curves 2-5 are at (a,b)=(265,-2959) [curve#4114], (80, 81205/4) [curve#1685], (165, 16215) [curve#1652], and (288, 60409/4).\r\n",
  "created_at": "2026-10-09 15:33:10",
  "updated_at": "2026-10-09 15:33:10"
}