{
  "id": 179,
  "curve_key": "247513232241433001838817:-124318869486488173260308264018173649",
  "ainvs": [
    "1",
    "1",
    "1",
    "-5156525671696520871642",
    "143887580422027574095483236694887"
  ],
  "rank_lower_bound": 16,
  "naive_height": 161.6163157236087,
  "faltings_height": 11.330767804286205,
  "conductor": "33158290302303235820773702112187496615798899795769945854",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "17",
    "31",
    "97771",
    "25996012748249",
    "27882505940647",
    "1034774277845385713"
  ],
  "discriminant": "-168881732015251142870523473594217561643594320461409532628190621696",
  "regulator": "3308054707823128.622854542820352955876197443222107463050585906051669328",
  "points": [
    [
      "1796235055657",
      "-2405486875415698453"
    ],
    [
      "280260196900225/361",
      "-4672441924825390438711/6859"
    ],
    [
      "33794917963577/49",
      "-195437004131314663299/343"
    ],
    [
      "276830759494257/1369",
      "-4348434658144756657809/50653"
    ],
    [
      "-1713074912095/169",
      "30688521194867715447/2197"
    ],
    [
      "4976539371434433/190969",
      "435305469622794811181391/83453453"
    ],
    [
      "150079661251/4",
      "14385645730349821/8"
    ],
    [
      "1209129808574197/24649",
      "11595110519046294355607/3869893"
    ],
    [
      "514060728091/9",
      "161327383722616421/27"
    ],
    [
      "4645811742356381/27889",
      "291137569948406847945789/4657463"
    ],
    [
      "36052656660133/81",
      "213816965792357845331/729"
    ],
    [
      "4850146428169",
      "10680334290818758187"
    ],
    [
      "176562964409213586197/4115607409",
      "336723416420365931137503833799/264028562109577"
    ],
    [
      "1170267928267",
      "-1263655175584965025"
    ],
    [
      "644082512583421135/96721",
      "-516876990947020027291331609/30080231"
    ],
    [
      "4995701755998585/5041",
      "352195399117596328279933/357911"
    ]
  ],
  "submitter": "Seewoo Lee",
  "commentary": "Rank ≥16. Mestre–Fermigier construction from the integer 6-tuple a=[-498, -216, -6, 414, 552, -246] with shift t=2577/4: 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 16:01:56",
  "updated_at": "2026-07-01 22:37:41"
}