{
  "id": 4579,
  "curve_key": "711847710619906922013309406883001:-18260173864782890483967390177684139074269266456749",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-14830160637914727541943945976729",
    "21134460491646867693613527739890379784909256285"
  ],
  "rank_lower_bound": 17,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 226.93625036633077,
  "faltings_height": 16.838261839357266,
  "conductor": "4834182615430193767926697907961349712388368645771199790890",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "53",
    "83",
    "101",
    "137",
    "251",
    "463",
    "467",
    "619",
    "647",
    "727",
    "907",
    "1277",
    "4447",
    "10039",
    "10987",
    "14011",
    "16553"
  ],
  "discriminant": "15786239236164557107876786021501242993888680609800034575422888562684601869255679900965556250000",
  "regulator": "123317795439149552188965.517288856627152635228516019510877111643676121147",
  "points": [
    [
      "-4408335659738354",
      "29012647655334870732927"
    ],
    [
      "-1615342248686829",
      "202176368362299562476252"
    ],
    [
      "109739561364771",
      "139672211700784115321052"
    ],
    [
      "1271733170241715",
      "65812110933599231168220"
    ],
    [
      "53200859178747047400378334/41810843529",
      "562207415056554768474247607661381537791/8549355852279333"
    ],
    [
      "-2559687006100854",
      "-205727894089296813429573"
    ],
    [
      "-2806674368438354",
      "-201614820954744953854573"
    ],
    [
      "4641064178068590",
      "-228632517395949888704685"
    ],
    [
      "4165247111125515",
      "-177840463457240921892900"
    ],
    [
      "608481769513232993661289/228856384",
      "-77386415027150076866713181399213321/3462139377152"
    ],
    [
      "39850322552088690135624819/15467150689",
      "10179855484213100164548988194022728351/1923603129738863"
    ],
    [
      "2742493760764771",
      "33013315341481888121052"
    ],
    [
      "2452425182763076733566/436921",
      "97824445755650154989570846059287/288804781"
    ],
    [
      "-41363978098205163846/11449",
      "203354331217799918335573928961/1225043"
    ],
    [
      "651291357891861318849/6400",
      "-16609484297393250412958909106153/512000"
    ],
    [
      "24539758433290182211/6241",
      "75764843096311426459279593828/493039"
    ],
    [
      "-285890208755559214101530709/114913542121",
      "-8043056166506930454475466877409773490587/38954426730055669"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Curve and independent-point witnesses from the Layr Labs Elliptic Rank Challenge public repository, submission/board/2-r17-z2k3.ec.\r\n\r\nSpecialization u = 4/5, t = -641/910 of the Elkies–Klagsbrun Z/2Z family (arXiv:2003.00077). The original submission describes Mestre–Nagao sieving followed by PARI/GP rank calculations.\r\n\r\nSubmitted to ICARM to document these improvements and make the curve available to other researchers.",
  "created_at": "2026-10-18 08:10:15",
  "updated_at": "2026-10-18 08:10:15"
}