{
  "id": 181,
  "curve_key": "191742524175704362767937:-86926153468796658699462910546782049",
  "ainvs": [
    "1",
    "0",
    "0",
    "-3994635920327174224332",
    "100608973921885468649536289354896"
  ],
  "rank_lower_bound": 16,
  "naive_height": 160.90073403262164,
  "faltings_height": 11.328963125180563,
  "conductor": "2612385923234423880735212879508736416654664660133355599474",
  "bad_primes": [
    "2",
    "13",
    "17",
    "31",
    "11959",
    "23251",
    "408088463",
    "1680206082665728718324081958011335561"
  ],
  "discriminant": "-293231918449934958705327201280235162673170146698422177169348591616",
  "regulator": "18179029818469538.42785326452085272304280545004754511587406136711446082",
  "points": [
    [
      "87115448112040/81",
      "811725076551771850436/729"
    ],
    [
      "54853647379656152/78961",
      "12795840505903551940628820/22188041"
    ],
    [
      "684286234212",
      "563721713419195768"
    ],
    [
      "2077475676535/36",
      "1704402380888340179/216"
    ],
    [
      "49957756120",
      "5072387202031156"
    ],
    [
      "46305881816",
      "3863202607195380"
    ],
    [
      "25675060780",
      "3869312490662116"
    ],
    [
      "19844421339720/361",
      "-47088243196964595284/6859"
    ],
    [
      "77021844495756/625",
      "-601082613854102469296/15625"
    ],
    [
      "176685692356",
      "-70075466002658780"
    ],
    [
      "391743880410598552/1771561",
      "-236149425639728063915026180/2357947691"
    ],
    [
      "33693387294",
      "2065506386879344"
    ],
    [
      "234291431845531154/6446521",
      "30331796260318243907203456/16367716819"
    ],
    [
      "20977572027526184/5329",
      "-3037926865430113221598380/389017"
    ],
    [
      "573999989640",
      "-432350725599294716"
    ],
    [
      "27445975192",
      "3412733323302388"
    ]
  ],
  "submitter": "Seewoo Lee",
  "commentary": "Rank ≥16. Mestre–Fermigier construction from the integer 6-tuple a=[-498, -216, -6, 414, 552, -246] with shift t=281/2: let p6(x)=∏(x−a_i) and q(x)=p6(x−t)·p6(x+t); completing q to g(x)²−r(x) gives the genus-1 quartic model y²=r(x), whose x=a_i±t base points plus a few small-x extra points supply 16 independent rational points. The shift t was selected by a Nagao–Mestre prime-sum sieve; the witness points were found by an integer quartic-point search and certified independent via the Néron–Tate height-pairing matrix.",
  "created_at": "2026-06-25 16:02:06",
  "updated_at": "2026-07-01 22:37:40"
}