{
  "id": 177,
  "curve_key": "2881085462060791782084961:-4875875892539662193674229076352817041",
  "ainvs": [
    "1",
    "0",
    "0",
    "-60022613792933162126770",
    "5643374875619607135973539223008900"
  ],
  "rank_lower_bound": 16,
  "naive_height": 168.96062805463853,
  "faltings_height": 11.894552101595167,
  "conductor": "18199850239630741806694632255103221302824470127647536470",
  "bad_primes": [
    "2",
    "5",
    "7",
    "13",
    "14143",
    "61095704479",
    "2023834707752971",
    "11436658788285881147191"
  ],
  "discriminant": "81438791243922645157611866031099042317832628278473480004951449600000",
  "regulator": "596245719370995.9770421874122669814731596437173131542981089055244318210",
  "points": [
    [
      "5249051824831780/9",
      "380295550092660091636810/27"
    ],
    [
      "2031681680938015/4",
      "91576372616636717841705/8"
    ],
    [
      "2844244702180/9",
      "3646219393118000650/27"
    ],
    [
      "290345255752",
      "112659987508580286"
    ],
    [
      "191998494861682180/1520289",
      "-16484070580180227559886050/1874516337"
    ],
    [
      "128168077282",
      "-7471078717004238"
    ],
    [
      "29107455924484/225",
      "22258797552123760418/3375"
    ],
    [
      "478620130398595780/4297329",
      "164229744232688785540957550/8908363017"
    ],
    [
      "1771839391525/16",
      "1205024210105889495/64"
    ],
    [
      "9629446541859620/19321",
      "-847256984370131499683750/2685619"
    ],
    [
      "1107272954531184/2209",
      "-33077154155676376659774/103823"
    ],
    [
      "1167606137791940/1681",
      "-37690495954067937504370/68921"
    ],
    [
      "1128217426980",
      "-1172179765340581410"
    ],
    [
      "115330085540",
      "15967736869394430"
    ],
    [
      "33583372397920",
      "-194614399746674405950"
    ],
    [
      "34375110789572",
      "-201537188908789628034"
    ]
  ],
  "submitter": "Seewoo Lee",
  "commentary": "Rank ≥16. Mestre–Fermigier construction from the integer 6-tuple a=[-498, -216, -6, 414, 552, -246] with shift t=7/8: 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 16:01:46",
  "updated_at": "2026-07-01 22:38:40"
}