{
  "id": 6085,
  "curve_key": "115850272477484051963972138062113805412298913:-1236916026004803169378189000871233279786880283892296663050030433905",
  "ainvs": [
    "1",
    "1",
    "1",
    "-2413547343280917749249419542960704279422894",
    "1431615770838892557149676069244967765505961218584294918413701611"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 304.3826175258322,
  "faltings_height": 23.22098886657961,
  "conductor": "781206292224258045638669835730061367474174860190703579746",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "19",
    "29",
    "79",
    "109",
    "229",
    "269",
    "389",
    "449",
    "727",
    "773",
    "1327",
    "2179",
    "2731",
    "14897",
    "22817",
    "72469",
    "2546329"
  ],
  "discriminant": "14408762850756776453683650180256071785671783989261206338220897759663794435279933212025243954276628898613641631354873204979073024",
  "regulator": "480108167456158.332950486728226314081251059109030090022581534529627",
  "points": [
    [
      "14201051616169454692655",
      "1682581616478834228343277428053717"
    ],
    [
      "-1227761369698203306891",
      "-50439577248985937030916337566665"
    ],
    [
      "-1432547749392475161293",
      "44150572412259747928989046205115"
    ],
    [
      "40350827152666016025198073/39601",
      "-43346865913654250895503292312704440655/7880599"
    ],
    [
      "1376546732755023974781713",
      "1615050711646726951322471525576630295"
    ],
    [
      "9991153646687740465553",
      "987251707759339727754337418403735"
    ],
    [
      "1010247597795307038705",
      "4939056025235211519099884600407"
    ],
    [
      "2187919434689532519622531/2209",
      "-370638346517058703393114225788857035/103823"
    ],
    [
      "1578857745036752095541",
      "39455436405665014533066149767479"
    ],
    [
      "9480269054941054985927129809/28547649",
      "-3938507955592900429131543243180381067574327/152530088607"
    ],
    [
      "6464603827269514399345/9",
      "223602326075196084946250759262349/27"
    ],
    [
      "224546729260882360232737745/452929",
      "-5758722490863736138841442862665502129161/304821217"
    ],
    [
      "71872310796946647104169/25",
      "16888388855583065082081322386480443/125"
    ],
    [
      "246085448561580066242714380443377/236535349801",
      "786166943423051513383149987919228970527299966123/115038730840366549"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Original specialization/search by kaankolcu (2026), public Yukon elliptic-rank challenge submission 1da657b4-8209-460d-8ef5-accfd1c896f3. Source: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/f034f33d9fd851c472e99fe31ef5e489469b171a/submission/board/2x2-14-own.ec . Specialization T=86513/4358 of the rank-five X312 family posted by wgxli with curve#4269: y^2=x(x+A)(x+B), A=-q(29p+2q)(400p+49q)(221p+86q), B=-p(8p+53q)(25p+88q)(392p+221q). The fourteen supplied points were checked exactly on the displayed model and certified independent modulo torsion by an exact rank-14 F_5 reduction matrix at fourteen good primes.",
  "created_at": "2026-10-29 01:05:59",
  "updated_at": "2026-10-29 01:05:59"
}