{
  "id": 6084,
  "curve_key": "710430989075479834657474735089976257397460800:-17176806505492227743834390223623923342566102561077050351118194240000",
  "ainvs": [
    "0",
    "1",
    "0",
    "-14800645605739163222030723647707838695780433",
    "19880563085060448777581166247325775999488608463734387145340057263"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 309.82333715545764,
  "faltings_height": 23.788740292499387,
  "conductor": "133653858380181200276790756551044378370721889766216757595200",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "23",
    "29",
    "43",
    "59",
    "67",
    "71",
    "83",
    "149",
    "157",
    "163",
    "191",
    "227",
    "233",
    "281",
    "431",
    "461",
    "829",
    "1049",
    "1531",
    "1609",
    "24439"
  ],
  "discriminant": "36759547906630277961861433909723215248315119298651779616919037536050649579589595091701695914877108579991002976700712374683904000000",
  "regulator": "1707984268136408.369182129207114624455197172848779595173017694098",
  "points": [
    [
      "-2618623969856750687902",
      "201696510682678989821254189946475"
    ],
    [
      "-722316508383335376361",
      "173765507231822410026506239227504"
    ],
    [
      "2776306230257068823783",
      "13742759104187222380004415712800"
    ],
    [
      "2783722246935065225762",
      "15844408676035048825412771159883"
    ],
    [
      "4924211549363933328509",
      "257683220788262571769909661096724"
    ],
    [
      "5570970445064635711583",
      "332153031701734321885089724803600"
    ],
    [
      "7633678703866949185943",
      "593072453367630818270520989691600"
    ],
    [
      "76276205795052393954527/49",
      "8492933658958190777416129473182400/343"
    ],
    [
      "1371928929750409538148823/81",
      "1568301922109102012402137434520192000/729"
    ],
    [
      "1669068760113619645151599/361",
      "1538056048780176833352722676385775184/6859"
    ],
    [
      "235277378919287717420863154/156025",
      "1940023439243390870053291367519315077983/61629875"
    ],
    [
      "2440070871172541499243972103/136161",
      "117935057517803869562573348304824667076000/50243409"
    ],
    [
      "1626808726033636567697457006167/2617038649",
      "13990514343229408762461692792492947214292993600/133879846166893"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Original specialization/search by 0xArion (2026), public Yukon elliptic-rank challenge submission 7e9f6673-cf5f-4cb9-82b4-a22add86d720. Source: https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/7482bf99c4a605a688f26c12d413f7085233dec2/submission/board/first-t2x2-p35213-q16986-r13.ec . Specialization T=35213/16986 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 source explicitly declares a material dependency on kaankolcu’s prior Yukon submission 43af8780-369f-484f-b8df-47147017654b for the family equations. The thirteen supplied points have been checked exactly on the minimal model and certified independent modulo torsion by an exact rank-13 F_7 reduction matrix at thirteen good primes.",
  "created_at": "2026-10-29 00:59:28",
  "updated_at": "2026-10-29 00:59:28"
}