{
  "id": 184,
  "curve_key": "56120036720384132570852719825:-13306901632518891887021252432213974169545625",
  "ainvs": [
    "1",
    "1",
    "1",
    "-1169167431674669428559431663",
    "15401506519118600679103992536133903673781"
  ],
  "rank_lower_bound": 16,
  "naive_height": 198.59371345224721,
  "faltings_height": 14.319878036317293,
  "conductor": "27848933853647946223887115529474676067564332131897391119550",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "29",
    "43",
    "73",
    "127",
    "10976906220863655801963668324973584199589113587"
  ],
  "discriminant": "-188601378345374742510097865390040902199163746431220797536602817961331170304000000",
  "regulator": "478580258045246.6958029338668409040983047906002491042699010978353959955",
  "points": [
    [
      "1963577490193219370285/100741369",
      "-4274287134927945750647758597824/1011141120653"
    ],
    [
      "19725482435915",
      "-3767596628797241358"
    ],
    [
      "44146965146747074355/2217121",
      "-13166106608227591906765664382/3301293169"
    ],
    [
      "84992020769165771/4225",
      "-1304507955376817204212926/274625"
    ],
    [
      "43475756338146835/1681",
      "-3420442022630210280753678/68921"
    ],
    [
      "5169927390880715/121",
      "-277434016070257283551698/1331"
    ],
    [
      "1045726115326939",
      "-33798511720116140751662"
    ],
    [
      "15690799565930621520315/8473921",
      "1965142616992608074707764709942702/24667584031"
    ],
    [
      "295490081647955",
      "5046826565144989978122"
    ],
    [
      "1957220904751499/25",
      "79422926794702239882258/125"
    ],
    [
      "134051813545315/9",
      "-970332229292678234186/27"
    ],
    [
      "23850116890041395/1369",
      "-906698356527892497902934/50653"
    ],
    [
      "17622325019835",
      "-16450132122712468718"
    ],
    [
      "18011746641515",
      "-13644940173569852958"
    ],
    [
      "2649576959335347595/88209",
      "2251205537386863546278362306/26198073"
    ],
    [
      "38852091226715",
      "-169184993480190893358"
    ]
  ],
  "submitter": "Seewoo Lee",
  "commentary": "Rank ≥16. Mestre–Fermigier construction from the integer 6-tuple a=[-1146, -2304, -654, 3054, 2880, -1830] with shift t=2919/8: 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 16:02:21",
  "updated_at": "2026-07-01 22:40:40"
}