{
  "id": 210,
  "curve_key": "704545914222730715359034280289:-515073146828791295390840612344745256877902737",
  "ainvs": [
    "1",
    "1",
    "1",
    "-14678039879640223236646547506",
    "596149475496280105667226784565254703843519"
  ],
  "rank_lower_bound": 11,
  "naive_height": 206.18205303849962,
  "faltings_height": 15.168483543162193,
  "conductor": "44702660536826547810138278991954523939494764170080309889431835489890",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "157",
    "2004720611",
    "630581423473",
    "255430951802014070304557438075659110521"
  ],
  "discriminant": "48857429671295622571237789586614535277793367429869518495768693667778413208750462668800",
  "regulator": "2751784961168.25749229920921519575526880971751709069524886858",
  "points": [
    [
      "58446067465881769",
      "-14129669742311093189766125"
    ],
    [
      "59805178857601951/9",
      "-14622998659211562714239875/27"
    ],
    [
      "41268971140291161/64",
      "-8243875117670686839240415/512"
    ],
    [
      "308108574052911809/841",
      "-162496149169433149662813345/24389"
    ],
    [
      "2136555534033197/16",
      "-64549605615325939384071/64"
    ],
    [
      "2447918870143671799281/27321529",
      "2428644462538774240003361334025/142809632083"
    ],
    [
      "91033697994269",
      "119840245127165271375"
    ],
    [
      "3579092917301768024617/34539129",
      "87981230877416815421786034759967/202986461133"
    ],
    [
      "8040116944201663249569/45010681",
      "578803785815401822474435058544295/301976658829"
    ],
    [
      "324903547043833",
      "5488603739649485397427"
    ],
    [
      "360854332952117",
      "6502958279889840406551"
    ]
  ],
  "submitter": "Seewoo Lee",
  "commentary": "Rank ≥11. Mestre–Fermigier construction from the integer 6-tuple a=[348, -600, -216, 492, 876, -900] with shift t=15681/13: 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 16:04:34",
  "updated_at": "2026-07-01 22:49:32"
}