{
  "id": 4578,
  "curve_key": "249961319680025788438998348182019925057761:-124952043159180417114535150704499030857814667683896834162189009",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-5207527493333870592479132253792081772037",
    "144620420323125482772754602596133271881701574364254541464061"
  ],
  "rank_lower_bound": 18,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 285.9663744341387,
  "faltings_height": 21.53936950160173,
  "conductor": "483328727128257581098535465545997674973027785591045803016636754582035590",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "37",
    "41",
    "43",
    "71",
    "113",
    "127",
    "131",
    "149",
    "337",
    "401",
    "1039",
    "1579",
    "16661",
    "22961",
    "32183",
    "131581",
    "162947",
    "164117",
    "1974221",
    "2835163"
  ],
  "discriminant": "2740435427455101380021539928002267778666061920104593483274276126046064428701780515269744168344540708205323348224000000",
  "regulator": "335830005340227485701.69921974272339952757245772931859592870143922435826272",
  "points": [
    [
      "6358319309605088281",
      "334314751790829581304985376084"
    ],
    [
      "17558963446770353161",
      "242064796724378451770274875924"
    ],
    [
      "23517000666444077731",
      "187512810289322774545749259484"
    ],
    [
      "37213695592889277631",
      "48629248975055082681326941184"
    ],
    [
      "38935176922128215191",
      "29801337270719666119519501064"
    ],
    [
      "42828689304899740831",
      "12221440968418976930084002784"
    ],
    [
      "52920621772315790431",
      "131316063340518690985767315584"
    ],
    [
      "69832634848090393591",
      "348583798108877321788040471264"
    ],
    [
      "132152956019021184031",
      "1328308267531781365638369075584"
    ],
    [
      "-43339503299083339434929/529",
      "1778105204750596803212751390405088/12167"
    ],
    [
      "-22042966266325234547369/361",
      "3324567550881589212800459797447616/6859"
    ],
    [
      "3053731267630061675269/49",
      "85496744685963375232591924800812/343"
    ],
    [
      "35393446809508652028151/841",
      "14468266905323310132788671919296/24389"
    ],
    [
      "113150318643740829710389/1369",
      "26746983044854126569113254368880502/50653"
    ],
    [
      "272351894660504881440063091/6630625",
      "78555455327815170373086462590296494164/17073859375"
    ],
    [
      "691396313439248446073102279/16785409",
      "167645667086400004300718062278445123232/68769820673"
    ],
    [
      "389198224543902574791763035481/9232903744",
      "2539150056478023646520456902151924601858233/887171254953472"
    ],
    [
      "118173422614763973620489369551/2402862361",
      "10176786080760171574435941271273323966971176/117785910073859"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Curve and independent-point witnesses from the Layr Labs Elliptic Rank Challenge public repository, submission/board/2-r18-z2k3.ec.\r\n\r\nSpecialization u = 4/7, t = -12673/12022 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 08:08:39",
  "updated_at": "2026-10-18 08:08:39"
}