{
  "id": 167,
  "curve_key": "207460182766946128527249:-97821106427688674280630047678889657",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-4322087140978044344318",
    "113218873181275746647084844047757"
  ],
  "rank_lower_bound": 16,
  "naive_height": 161.1368968694085,
  "faltings_height": 11.348512992830234,
  "conductor": "56059062740283999533055887298056005020483418801410",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "19",
    "23",
    "43",
    "6529",
    "1327973",
    "2253551",
    "11863534244867284689946519"
  ],
  "discriminant": "-370335152258882249448312295653484868140997279261599897092748492800",
  "regulator": "129652450970271.3285372382617348758143858676004025284640855566598266686",
  "points": [
    [
      "4932628938917",
      "-10954167952365331425"
    ],
    [
      "446184178743003/196",
      "-9420897930023067416333/2744"
    ],
    [
      "9544497553624449113/5909761",
      "-29462901095704390278748461027/14366628991"
    ],
    [
      "230856486055446737/259081",
      "-110627478320435505484822737/131872229"
    ],
    [
      "687244594339217/1369",
      "-17869337246424980997321/50653"
    ],
    [
      "111714407682185/358801",
      "2273230596607997710939317/214921799"
    ],
    [
      "20777055868853/841",
      "113138478760251712407/24389"
    ],
    [
      "4297326630785/121",
      "2828314365172462761/1331"
    ],
    [
      "38392883723",
      "1968003627921723"
    ],
    [
      "43458840423",
      "2732270569874853"
    ],
    [
      "205418185807217/3481",
      "1638702900632091787593/205379"
    ],
    [
      "1009339707253977/11881",
      "24543070374389616153303/1295029"
    ],
    [
      "50577086539596065/434281",
      "9870335059605680578829697/286191179"
    ],
    [
      "257718003905",
      "126951044297053971"
    ],
    [
      "686682213293",
      "566513798751435243"
    ],
    [
      "50399148128803/36",
      "357407945712747949543/216"
    ]
  ],
  "submitter": "Seewoo Lee",
  "commentary": "Rank ≥16. Mestre–Fermigier construction from the integer 6-tuple a=[-1146, -2304, -654, 3054, 2880, -1830] with shift t=1929/1: 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 16:00:56",
  "updated_at": "2026-07-01 22:37:41"
}