{
  "id": 176,
  "curve_key": "1893955373637317153023329:-2587884603326693689092916058758460817",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-39457403617444107354653",
    "2995236809415759824391532391142437"
  ],
  "rank_lower_bound": 16,
  "naive_height": 167.70212899313364,
  "faltings_height": 11.825872743039886,
  "conductor": "6430563811515979376580169926167902717057516739737835010",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "19",
    "1003771",
    "997188134941985254983271503747820602358073"
  ],
  "discriminant": "55901631537054437994489290286441257543068900330119374782386280857600",
  "regulator": "1807850498928697.709773358085301962190248467956461960084294927955712660",
  "points": [
    [
      "144809072073313",
      "1742582023374680171298"
    ],
    [
      "119013030166267/9",
      "1298204132495509294076/27"
    ],
    [
      "14453193394137/64",
      "38320836532964296481/512"
    ],
    [
      "82737779887",
      "-17233834740637208"
    ],
    [
      "1625900049957/16",
      "-378511156915988195/64"
    ],
    [
      "99883404201318583/942841",
      "-1858606599514605068981832/915498611"
    ],
    [
      "94373439663",
      "10584301043120488"
    ],
    [
      "1456550150901/16",
      "803654378416531621/64"
    ],
    [
      "118824023111096415/1456849",
      "31435043139868783893538264/1758416743"
    ],
    [
      "664284748380235207/2036329",
      "-457969898199541897508533896/2905841483"
    ],
    [
      "11055538290343/9",
      "-36305826547177738760/27"
    ],
    [
      "1440208560111",
      "-1712732440197729176"
    ],
    [
      "9113382082811474679/4644025",
      "-27376005199713547093247578952/10007873875"
    ],
    [
      "307862534703",
      "-141516189959116952"
    ],
    [
      "50770409072312721919/1103767729",
      "1310741387619272185155970466008/36670475260567"
    ],
    [
      "13914484586320425535951/28771283641",
      "-1520159124306311998316785261631576/4880213902470061"
    ]
  ],
  "submitter": "Seewoo Lee",
  "commentary": "Rank ≥16. Mestre–Fermigier construction from the integer 6-tuple a=[348, -600, -216, 492, 876, -900] with shift t=2913/4: 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 16:01:41",
  "updated_at": "2026-07-01 22:38:39"
}