{
  "id": 6087,
  "curve_key": "23008222197889451573743918742443253056:-109748735870014274491733007632246667153749994573230088704",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-479337962456030241119664973800901105",
    "127023999849553558599285116689332611801173040541538897"
  ],
  "rank_lower_bound": 18,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 258.08674496008905,
  "faltings_height": 19.347528444539915,
  "conductor": "1267548066931185496991495042988782951726511449140210157873613120",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "23",
    "29",
    "31",
    "43",
    "53",
    "61",
    "113",
    "127",
    "149",
    "271",
    "373",
    "433",
    "769",
    "827",
    "863",
    "1033",
    "1453",
    "1657",
    "2053",
    "6991"
  ],
  "discriminant": "78280247831823416883598446566167686668640237781810624016601302065529866200279962668787687229670123776000000",
  "regulator": "608636445643439864696.04743513237272393730983686000833748258157763341740456",
  "points": [
    [
      "2258983854455671645861/5329",
      "775515975451240293876447955680/389017"
    ],
    [
      "-16259614282986063977381/84681",
      "11345646119852791598566786157298500/24642171"
    ],
    [
      "6649760696320392856/49",
      "-87092757280339230083992365885/343"
    ],
    [
      "374496806071164549",
      "-5986540705489264141466000"
    ],
    [
      "1811540234946930799",
      "-2281134755165392558287534000"
    ],
    [
      "62204067856959549",
      "-312166490468264236365316000"
    ],
    [
      "11864257234598248588981/34969",
      "384043582713796052296516051848000/6539203"
    ],
    [
      "1328604131142040377566149/3806401",
      "-351359047261492192486914840700770000/7426288351"
    ],
    [
      "15059549584431863701459/3025",
      "1831069915435756430061215947024548/166375"
    ],
    [
      "19530944830979009070502501/123054649",
      "-319965281520484122258514606858649228400/1365045221357"
    ],
    [
      "400241233501201929364149/1079521",
      "-18448992523719271069218438054502720/1121622319"
    ],
    [
      "12962625638690360186893/34969",
      "108477005066850132231214113111072/6539203"
    ],
    [
      "548292344516115306799/9025",
      "268574954335610483796405808415568/857375"
    ],
    [
      "154389926241967830667111/100489",
      "55332345305337478226120762555746800/31855013"
    ],
    [
      "243003771145938471080109/697225",
      "-27904664342130142271990831374940048/582182875"
    ],
    [
      "774434750215117197",
      "-469334244269555516353513424"
    ],
    [
      "706822451155086558406477/1560001",
      "104127674475601395333181424201626704/1948441249"
    ],
    [
      "90333173155162165286269231/2765569",
      "858369167222904725305249916411286832800/4599141247"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Original specialization/search by kaankolcu (2026), public Yukon elliptic-rank challenge submission ddb44e4a-f316-457b-a3f2-7316d2cc04d4. Source: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/236fa93f21f753f95316d5a2449371577693fbb6/submission/board/2-18-own.ec . Specialization T=30/769 of the rank-nine X808 fibration posted by wgxli with curve#4078: y^2+84(35397T^2-221T+20)xy=x(x+F)(x+G), F=(1139T+115)(1269T-59)(3776T+34)(539T-5), G=8(638T-23)(250T-1)(7811T+499). The eighteen supplied rational points were checked exactly on the minimal model and certified independent modulo torsion by an exact rank-18 F_5 reduction matrix at eighteen good primes.",
  "created_at": "2026-10-29 01:30:53",
  "updated_at": "2026-10-29 01:30:53"
}