{
  "id": 189,
  "curve_key": "7950451352554236973757463169:-691075060315003274769578092099529022607297",
  "ainvs": [
    "1",
    "0",
    "0",
    "-165634403178213270286613816",
    "799855393883091839227487570305634706496"
  ],
  "rank_lower_bound": 17,
  "naive_height": 192.72907863540027,
  "faltings_height": 13.967463280553337,
  "conductor": "8541964435847820105889019133681263942251915526797299744486693070",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "13",
    "31",
    "963617201",
    "156542453132674409",
    "182484217080500391795285792738533"
  ],
  "discriminant": "14444861515529646982364107927886725142451411941867709623555198879792460966963200",
  "regulator": "174183243424871196.117456918605717418856645255314545313199949862786374577",
  "points": [
    [
      "3771724805693216/25",
      "-230820834416887219151576/125"
    ],
    [
      "220650513021776144/2209",
      "-102825180245912272434259304/103823"
    ],
    [
      "58363265298704",
      "-435814179298469087992"
    ],
    [
      "121206730250907905696/4490161",
      "-1203454835017313260439695009672/9514651159"
    ],
    [
      "22736561402976",
      "-93742167691902387368"
    ],
    [
      "89987241840089645664/5678689",
      "-628103463007840626180227153096/13532315887"
    ],
    [
      "564525651073621876/63001",
      "93736751901381586320629692/15813251"
    ],
    [
      "1449414454105204150/151321",
      "564974171284448928893290084/58863869"
    ],
    [
      "273661363709014/25",
      "2159293870027528337902/125"
    ],
    [
      "13964147866804",
      "34783393964917112948"
    ],
    [
      "833419877491021060/56169",
      "533954318650346565473505592/13312053"
    ],
    [
      "11612977777536",
      "-21035392256727489208"
    ],
    [
      "3226174044596208007696/47045881",
      "180219935774189259169905542093208/322687697779"
    ],
    [
      "573546865748084535976/11215801",
      "-13336036910237094494990068561432/37561717549"
    ],
    [
      "43838486531548",
      "-278905136311491012660"
    ],
    [
      "5538299763932867296/477481",
      "6914201219537011087158124872/329939371"
    ],
    [
      "12688301446408259420456/1434818641",
      "-280680749199495086182087317126472/54349495302439"
    ]
  ],
  "submitter": "Seewoo Lee",
  "commentary": "Rank ≥17. Mestre–Fermigier construction from the integer 6-tuple a=[348, -600, -216, 492, 876, -900] with shift t=3023/1: 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 17 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 16:02:47",
  "updated_at": "2026-07-01 22:36:40"
}