{
  "id": 6089,
  "curve_key": "95192355536418604709917617090375848024707716025:-28694206088627353593378008292907136964766344304895346331415608270286125",
  "ainvs": [
    "1",
    "0",
    "1",
    "-1983174073675387598123283689382830167181410751",
    "33210886676652029621965122111543787426920462301469572647735614824898"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 324.5166864729541,
  "faltings_height": 24.94562872004242,
  "conductor": "1054762203308866304488003670795381982678824380721354006581950",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "31",
    "47",
    "59",
    "61",
    "71",
    "79",
    "83",
    "89",
    "139",
    "151",
    "179",
    "181",
    "193",
    "503",
    "593",
    "5039",
    "6949",
    "7561",
    "10111",
    "50273"
  ],
  "discriminant": "22706085298105540554968955502130849484032585220525321783507184187758525699603339681916012406031655260277297683450700030543910299006250000",
  "regulator": "2669248480249460334.43502577059925592285144741483807871314536994999",
  "points": [
    [
      "89338780633400283871623/4",
      "1938354501474669316408825864237373/8"
    ],
    [
      "29093805220076669485812",
      "373153326112278330322033873648906"
    ],
    [
      "35001872427322941823587",
      "2584175359209977713050104965457956"
    ],
    [
      "-167431725844097109131734633426362257637/17272027533763396",
      "16293776248283353762719394292249089706882464952937632058769/2269943159964154696160056"
    ],
    [
      "-1503405948439192904810045196370044613/62000994113041",
      "3997341169785844312034005535513982543210656130050783856/488200229716666859911"
    ],
    [
      "-58341218742926603485952523377413917/1305335955169",
      "8510781580875210503956417291667008913880467853831512/1491363298147999697"
    ],
    [
      "-88245049346175285505424930433/1745041",
      "4713856968854908955411196644008173468965416/2305199161"
    ],
    [
      "485770177878009096762837/16",
      "63548163295194682669878905395983469/64"
    ],
    [
      "375489129816399551904675612/22201",
      "7022859593754668975211187862853948717869/3307949"
    ],
    [
      "1080533600922701233921795144347/1681",
      "1123200824861917936725422912538199930611388676/68921"
    ],
    [
      "7505756336139814140671434065259702/337025530521",
      "58755771049472230817161331012807359046458689875339/195656464463130819"
    ],
    [
      "94119593044164170242658968762683907/5090862614436",
      "19443491151748158824405944640535210668167919450559329/11486482771776260184"
    ],
    [
      "4344426156219278457187699739247725958/150300317648209",
      "355985109229298934178148060368172415197168378002369487/1842637255172700821927"
    ],
    [
      "3341180616609314229247874527767938335518/79499054544558289",
      "110035854439871019576131411477362350686324290795992729166328/22415216899885768051202663"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Original specialization/search by 0xArion (2026), public Yukon submission branch 6b4e2dad-5978-4fed-8bbc-4abc0b0d4110. Source: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/e9e417b086d2c063187a39b214af3e38db1d807f/submission/board/2x2-14-p96576-q9845.ec . Specialization T=96576/9845 of the rank-five X400a family posted by wgxli with curve#4252: y^2=x(x+A)(x+B), A=q(121q-99p)(26p-23q)(75p-44q), B=p(21q-74p)(25p-36q)(p+77q). The companion source note credits the family equations through kaankolcu submission43af8780-369f-484f-b8df-47147017654b and reuses 0xArion section methods from submission7e9f6673-cf5f-4cb9-82b4-a22add86d720. The fourteen supplied points have been checked exactly on the minimal model and certified independent modulo torsion by an exact rank-14 F_5 reduction matrix at fourteen good primes.",
  "created_at": "2026-10-29 01:46:56",
  "updated_at": "2026-10-29 01:46:56"
}