{
  "id": 626,
  "curve_key": "8757694876923775508381266823958721:-613442721819278218538866218950317441901175299796769",
  "ainvs": [
    "1",
    "0",
    "0",
    "-182451976602578656424609725499140",
    "710003150253794219215652666162794189038512805392"
  ],
  "rank_lower_bound": 22,
  "torsion": [],
  "naive_height": 234.46572239166068,
  "faltings_height": 17.55872932242803,
  "conductor": "5651319165610115296564894984823807468501395910978185811787187868498410205790",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "19",
    "29",
    "71",
    "2465779087453622652131442949",
    "519784438179112504122441050306814600881"
  ],
  "discriminant": "170936848285991366957118762195218257884358220481825423891549871859917613495299194842452393152000000",
  "regulator": "1539741648619753344327.838064369512191998122834483177809266655540131523115768744816",
  "points": [
    [
      "-3428955858517076344/2209",
      "-103275287379914878066351333436/103823"
    ],
    [
      "341451890018744865176/100489",
      "11453652699578302486870011699484/31855013"
    ],
    [
      "1421989050733709804/1681",
      "-51403653211404431079338658392/68921"
    ],
    [
      "54938084184407822",
      "12510003464734650235120280"
    ],
    [
      "78266781050788904",
      "21583976314861037737936028"
    ],
    [
      "1576838726662055144",
      "1979999227161508319030537948"
    ],
    [
      "275856238766592504006794/133225",
      "144882186604686128205773785854751048/48627125"
    ],
    [
      "32343362505256116953036/4489",
      "5816704343975764908258919803727544/300763"
    ],
    [
      "451685153382923636/289",
      "3216654481209820295439953644/4913"
    ],
    [
      "159880614487269527391176/37393225",
      "-20535320605070024923156727491612396/228659570875"
    ],
    [
      "-207063576767969910796/25921",
      "-5373215212229459128185363202772/4173281"
    ],
    [
      "63431781447715124",
      "15632027594258343566588588"
    ],
    [
      "-14726457028992856",
      "450742903005235879493948"
    ],
    [
      "-25547628719315830766/16641",
      "2132137788731395250384172645382/2146689"
    ],
    [
      "816995985903150650526626/4489",
      "738464942904456142122944383416294434/300763"
    ],
    [
      "403133816812318948/9",
      "245103819466924941678683696/27"
    ],
    [
      "-21180060288786392556548096/1431789921",
      "-22466095285091040253863758892269050628/54177498820719"
    ],
    [
      "-2891729672233387873/196",
      "-1197251284734026121558242045/2744"
    ],
    [
      "-4452688329359660425432/316969",
      "126297560544003373654469422999060/178453547"
    ],
    [
      "-38963064251172216262504/2798929",
      "-3479733264232670937714460369607204/4682608217"
    ],
    [
      "-12896965910595856",
      "-958073803358837270715052"
    ],
    [
      "-4209096890749151344/529",
      "-15666577260849429714360102164/12167"
    ]
  ],
  "submitter": "Roy van Rijn",
  "history": [],
  "commentary": "This curve was found as a rational specialization, at parameter \\(t=3/17\\), of an elliptic-curve family of generic rank 16.\r\n\r\nWe found 22 independent rational points on the specialized curve, proving that its Mordell–Weil rank over \\(\\mathbb{Q}\\) is at least 22. The exact rank is not currently known.\r\n\r\nThe submitted equation is a global minimal Weierstrass model. Its conductor was computed and independently certified to be\r\n\r\n5651319165610115296564894984823807468501395910978185811787187868498410205790.\r\n\r\nThe factorization and local reduction data used in the conductor calculation, as well as exact certificates for the 22 independent points, are available in the accompanying research repository.",
  "created_at": "2026-09-07 07:58:17",
  "updated_at": "2026-09-07 07:58:17"
}