{
  "id": 183,
  "curve_key": "15513705481996191519473155825:-1906469079706956357141039555142704471175625",
  "ainvs": [
    "1",
    "1",
    "1",
    "-323202197541587323322357413",
    "2206561434845879634664264564474894007531"
  ],
  "rank_lower_bound": 16,
  "naive_height": 194.7345641061391,
  "faltings_height": 14.10580842990803,
  "conductor": "26383630742301813121429708006989650772225567353794271438550",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "37",
    "191",
    "199",
    "727",
    "971",
    "2300968998537812671658704438428873760173181"
  ],
  "discriminant": "57371302902497504412701897991058097709584123040592403193410870194441105536000000",
  "regulator": "3263598764701149.083111521840587555373665639651653710373481275686837503",
  "points": [
    [
      "180924565545781/9",
      "1671651863450906696876/27"
    ],
    [
      "10284908500556285015/410881",
      "26073080629552408556365503132/263374721"
    ],
    [
      "40246669791815",
      "233216790682242992892"
    ],
    [
      "514132005303891/4",
      "11549195090794268836181/8"
    ],
    [
      "43617102608779015/289",
      "9047390518527546741124316/4913"
    ],
    [
      "6630479150425740485/961",
      "17073238029898484032493832762/29791"
    ],
    [
      "982353939816655",
      "-30784333888025912219828"
    ],
    [
      "366922387740479",
      "-7020194305998509901012"
    ],
    [
      "5076217626798439755/44521",
      "-11302507691667110491785987368/9393931"
    ],
    [
      "4254910515588735/361",
      "-40307285259491291477612/6859"
    ],
    [
      "1036183133024957815/89401",
      "-111930322750105636756280092/26730899"
    ],
    [
      "2518861545901311335/214369",
      "554226264746709541557734724/99252847"
    ],
    [
      "305995178478481/25",
      "1147752566954104940114/125"
    ],
    [
      "12454361849885",
      "10634580957552665982"
    ],
    [
      "6677202029640505315/316969",
      "12294351622120792432232250204/178453547"
    ],
    [
      "247425027171655",
      "3881930663163099914172"
    ]
  ],
  "submitter": "Seewoo Lee",
  "commentary": "Rank ≥16. Mestre–Fermigier construction from the integer 6-tuple a=[-110, 6, 60, 44, 94, -94] with shift t=3303/11: 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 16:02:17",
  "updated_at": "2026-07-01 22:40:39"
}