{
  "id": 459,
  "curve_key": "92557521906549224707846809213815612401:-899659677205023268842466096461409987885944600686241078601",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1928281706386442181413475191954491925",
    "1041272774542851005444015987964798785676127762575830625"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 262.28322315410463,
  "faltings_height": 19.722894813659455,
  "conductor": "306630491920777660800789905311462621887091488323154470032105508244122033478180321990",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "37",
    "53",
    "853",
    "723071",
    "1031813399",
    "4250256977",
    "33664961833630290267498865544386230765212873423"
  ],
  "discriminant": "-9523712949064575272159815189891085656872405169059420712094224530887379514870038402491873816813367453696000000",
  "regulator": "770691786839733960707.601050797337180166880488833030170375156158952417938886978",
  "points": [
    [
      "776096304873893650",
      "-110467382469190686452369225"
    ],
    [
      "3249383160353677630",
      "5392970355484074740412071395"
    ],
    [
      "-1493698116763758350",
      "-767400011165300134180524425"
    ],
    [
      "383822445707741050",
      "598079902462208890594978375"
    ],
    [
      "263425887055935250",
      "742693355349190190997995575"
    ],
    [
      "742054005217641490",
      "137808945671122395835505335"
    ],
    [
      "8003725435241809090/9",
      "-4657794000112840877711462995/27"
    ],
    [
      "502437414977501650",
      "446395436373181106434475575"
    ],
    [
      "-5049530415477656705/4",
      "-9678865113552357282334340515/8"
    ],
    [
      "802096136354440210",
      "103153303705612373479522615"
    ],
    [
      "469837175643031570",
      "488885955225081533297521975"
    ],
    [
      "701802284745361810",
      "-183456951927329020143910985"
    ],
    [
      "949766844277928050",
      "-258067102581468619502683625"
    ],
    [
      "1279452454398048850",
      "-817673448591136098129588425"
    ],
    [
      "-10134597024761813150/9",
      "-36070678071480945395413159475/27"
    ],
    [
      "825899050877540650",
      "109818573493868614431108775"
    ],
    [
      "1492769253713359450",
      "-1220336221580496334593699425"
    ],
    [
      "10353218732586035100850/961",
      "-1045102686364836180490864570393175/29791"
    ],
    [
      "983770841715007720",
      "310457507940596917359802975"
    ],
    [
      "1843761613903631250",
      "-1937464607926962836124004425"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = -45/23. The 3 points beyond the seventeen generic sections came from searching the 1311 norm-4 quartic covers of the Mordell-Weil lattice; the claimed lower bound is rank >= 20.",
  "created_at": "2026-08-30 15:57:08",
  "updated_at": "2026-08-30 15:57:08"
}