{
  "id": 169,
  "curve_key": "601880103383413571773456:-466913491910981870868697429797800896",
  "ainvs": [
    "0",
    "1",
    "0",
    "-12539168820487782745280",
    "540409134152049294268977949499028"
  ],
  "rank_lower_bound": 16,
  "naive_height": 164.26303564359932,
  "faltings_height": 11.37127205732163,
  "conductor": "2411607429845182224131866326159229163946583369283280",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "397",
    "2467691",
    "11209488223933",
    "6398707603623935148158719"
  ],
  "discriminant": "16592587422778666947058928147605996735160005448846489950560000000",
  "regulator": "165765328977244.6178705897496116157230940079152440760508150581557650129",
  "points": [
    [
      "647952695791",
      "514250743863915630"
    ],
    [
      "28807123943701756/67081",
      "4737436060388057145083250/17373979"
    ],
    [
      "402262930006",
      "246147779511433260"
    ],
    [
      "276874758276076/1521",
      "3885218349856161135290/59319"
    ],
    [
      "6505232023429951/579121",
      "-8824954679706139266996990/440711081"
    ],
    [
      "11163916115709526/219961",
      "-608011399464814507106580/103161709"
    ],
    [
      "57498275851",
      "-3085582681209600"
    ],
    [
      "750610349688556/11881",
      "-800744222870078099250/1295029"
    ],
    [
      "64222059796",
      "5807235473910"
    ],
    [
      "34850173328686/361",
      "-103930279989431903700/6859"
    ],
    [
      "407905078926",
      "-251586046292995500"
    ],
    [
      "841209759076",
      "-765023428267291050"
    ],
    [
      "77470115910364/9",
      "-681812157670903246130/27"
    ],
    [
      "3572373541773499774/196249",
      "-6751917052827679352774129700/86938307"
    ],
    [
      "14946749973459694/625",
      "-1827323343746079478328628/15625"
    ],
    [
      "74724941345461609/73984",
      "20306169030417705203904075/20123648"
    ]
  ],
  "submitter": "Seewoo Lee",
  "commentary": "Rank ≥16. Mestre–Fermigier construction from the integer 6-tuple a=[-498, -216, -6, 414, 552, -246] with shift t=2892/5: 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 16:01:06",
  "updated_at": "2026-07-01 22:38:39"
}