{
  "id": 6090,
  "curve_key": "25452087520554712346683528062343225:-4028495618715117076376252540121906905201274047654125",
  "ainvs": [
    "1",
    "0",
    "1",
    "-530251823344889840555906834632151",
    "4662610669809163238655232938992868501361090224698"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 237.66631749845854,
  "faltings_height": 17.660523855565803,
  "conductor": "176767773759214183330795954037255316905199450",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "29",
    "43",
    "59",
    "67",
    "229",
    "383",
    "421",
    "449",
    "2357",
    "2689",
    "3389",
    "3943",
    "6311",
    "26951"
  ],
  "discriminant": "150062664677126979912499363523602717564908962224849039931331616964566267665117629271709953225000000",
  "regulator": "282806393045.78914705804919953124316301454759889275608348149430",
  "points": [
    [
      "15141542066359071",
      "324385023498662502880036"
    ],
    [
      "63261472779400203/4",
      "3855930182870274949795043/8"
    ],
    [
      "15937627958664951",
      "509842269190522744699492"
    ],
    [
      "69299204608735607",
      "17341213262736004045496196"
    ],
    [
      "185666733913702482",
      "79413735519369962395954321"
    ],
    [
      "-4125566531201819913/361",
      "20838115571003502431823399244/6859"
    ],
    [
      "-2042773066518952964/81",
      "1029728796856227435624145793/729"
    ],
    [
      "139434016767277078/9",
      "11006872764154083643079432/27"
    ],
    [
      "917203735285276572/121",
      "1382415809108761495075550126/1331"
    ],
    [
      "53789318156955902862/5041",
      "167692778793674232420709888631/357911"
    ],
    [
      "99185178956583917967/18769",
      "3643762399526750559309063489092/2571353"
    ],
    [
      "125710893444788912285487/13845841",
      "39798558273260242621425689227705756/51520374361"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Source parameter/search by bufferhe4d (2026), public Yukon submission 15009775-297e-4a19-9179-4a455b778310: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/6837b3bcd53a73fb5af3e271d91dec3148236631/submission/search/x400a-opus/xlog.txt . The source log records rank12 at T=181632/180163 in 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 published section code credits 0xArion submission7e9f6673-cf5f-4cb9-82b4-a22add86d720. Using its four selected sections, a local seeded PARI/GP replay recovered the twelve displayed points and bounds[12,12]. Every coordinate was checked exactly on the minimal model; independence modulo torsion was separately certified by an exact rank-12 F_5 reduction matrix at twelve good primes.",
  "created_at": "2026-10-29 02:00:36",
  "updated_at": "2026-10-29 02:00:36"
}