{
  "id": 171,
  "curve_key": "11665590134154724806987361:-39800787938347911381207104056415738641",
  "ainvs": [
    "1",
    "0",
    "0",
    "-243033127794890100145570",
    "46065726780475015041673462927320900"
  ],
  "rank_lower_bound": 16,
  "naive_height": 173.1560571786167,
  "faltings_height": 12.205848283826699,
  "conductor": "17001080899169472351595692437551130728110858780220870",
  "bad_primes": [
    "2",
    "5",
    "17",
    "19",
    "31",
    "1217",
    "1493",
    "177263817121",
    "141808312780621",
    "3717407278939619"
  ],
  "discriminant": "1979571123617220930817947516260302552311906430241986844098656704000000",
  "regulator": "503061140161974.4973933639952823682345584297528562360756791803810313595",
  "points": [
    [
      "804935286279771142485/2640726544",
      "-2376316883463090509738789991615/135701655643072"
    ],
    [
      "207118739029424340/436921",
      "-55839103538713816321049370/288804781"
    ],
    [
      "13398478215906/25",
      "-33013515993024297636/125"
    ],
    [
      "6136628085887340/10201",
      "-353267915888726695810770/1030301"
    ],
    [
      "815682344620",
      "-624926083455239770"
    ],
    [
      "241827032650000350/11881",
      "-118886100875419521952688880/1295029"
    ],
    [
      "73377184147540",
      "-628538393730579188770"
    ],
    [
      "337531713230",
      "49885061341813890"
    ],
    [
      "965139932699684/3025",
      "5269925999304849389538/166375"
    ],
    [
      "744546149483840/2401",
      "2685159731120074344270/117649"
    ],
    [
      "1591318012724410480/5294601",
      "159323126319820860385838630/12182876901"
    ],
    [
      "24442710167551460/83521",
      "58393952082645620285070/24137569"
    ],
    [
      "2499390306144935/7396",
      "-31985792865062494405965/636056"
    ],
    [
      "20253971560627616260/66601921",
      "-9123104136005428826183866290/543538277281"
    ],
    [
      "2642069083118124063920/8657744209",
      "-14395846477111130735943458783230/805577125414823"
    ],
    [
      "89533067998948/9",
      "-846158145396445374118/27"
    ]
  ],
  "submitter": "Seewoo Lee",
  "commentary": "Rank ≥16. Mestre–Fermigier construction from the integer 6-tuple a=[-138, 138, 162, -60, -90, -12] with shift t=1355/2: 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 16:01:16",
  "updated_at": "2026-07-01 22:39:38"
}