{
  "id": 211,
  "curve_key": "103895420219460887976030758560849:-1059351374675894073952680990935796750743854909657",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2164487921238768499500640803351",
    "1226101128097099442256424377019056466085320681"
  ],
  "rank_lower_bound": 11,
  "naive_height": 221.1634825477226,
  "faltings_height": 16.165246271644328,
  "conductor": "76884160347970864077673900010863037738725767115232422182209303915570",
  "bad_primes": [
    "2",
    "5",
    "7",
    "13",
    "17",
    "23",
    "31",
    "157",
    "33196799",
    "2096948303",
    "1944251946437",
    "25233503438885314304619774163"
  ],
  "discriminant": "-434796625061430848546124049916980604145395749660512866802185034140618458039551190139699200",
  "regulator": "6574796646890.56238082668096592613712251120723802057237124620",
  "points": [
    [
      "193471633301052616639334/1352569",
      "-85094808570897910903821838655812881/1573037747"
    ],
    [
      "405207134144905894/9",
      "-257802161495288662231116521/27"
    ],
    [
      "550091167141970389100/130321",
      "-12204497223776414581241469614979/47045881"
    ],
    [
      "209300708887435110/361",
      "88389056748088433517564679/6859"
    ],
    [
      "793448046452518",
      "2866253390847396035317"
    ],
    [
      "846049037447238",
      "662750304475737010357"
    ],
    [
      "7900678100479420/9",
      "42649563397126798370693/27"
    ],
    [
      "1030036895154710",
      "9457437854839529239509"
    ],
    [
      "1710543209524774",
      "50285471431872021894373"
    ],
    [
      "2517886218947724",
      "108346380885156670615183"
    ],
    [
      "51824229593028927046/15625",
      "341289027873148644301074534281/1953125"
    ]
  ],
  "submitter": "Seewoo Lee",
  "commentary": "Rank ≥11. Mestre–Fermigier construction from the integer 6-tuple a=[348, -600, -216, 492, 876, -900] with shift t=2326/23: 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 11 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 16:04:39",
  "updated_at": "2026-07-01 22:49:33"
}