{
  "id": 6093,
  "curve_key": "768952394386442853792510796004396774744329:-658585284801772791229010111188892221643624462623938920394280933",
  "ainvs": [
    "1",
    "0",
    "1",
    "-16019841549717559454010641583424932807174",
    "762251487039088878735945234487630274725620019016125376426116"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 289.33754306546336,
  "faltings_height": 22.01461050192117,
  "conductor": "114103645867500682535751079990457905333656368701852230",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "29",
    "31",
    "37",
    "53",
    "73",
    "79",
    "101",
    "107",
    "163",
    "173",
    "181",
    "229",
    "271",
    "281",
    "367",
    "463",
    "509",
    "691",
    "1163",
    "8887"
  ],
  "discriminant": "12116655417294506724487067006719893640138228080923445645031944877742036769444156386803484175768882679761907066289687000100",
  "regulator": "161881321413399.4481702196355366231964734657070231866002914006708",
  "points": [
    [
      "-131252575157858578654",
      "777031228505537957839595170077"
    ],
    [
      "-67147583879024772892",
      "1239027944808352742309123588268"
    ],
    [
      "39549235010832527660",
      "436508451105217225093570363767"
    ],
    [
      "61892176611835632833",
      "88517604990529838294653891023"
    ],
    [
      "254875953349476204827/4",
      "110115120710285041065208177599/8"
    ],
    [
      "94926455997781744106",
      "311335896221864833733303170896"
    ],
    [
      "145396218575344237271",
      "1227481951998366728448872900427"
    ],
    [
      "-63503867479316626806276495524473/1038538313569",
      "1301909739439335864781459182584801580227717697429/1058360894360091503"
    ],
    [
      "-1658755185287313605112652654/12453841",
      "32089716048725894031013799626343909058144/43949604889"
    ],
    [
      "-289425569065675792910008/2209",
      "81221970351954089685905503952137884/103823"
    ],
    [
      "96674615104871941982417/1024",
      "9901423488723660823379865279079689/32768"
    ],
    [
      "3010590946052200914867278/11881",
      "4664482237066542807757715548483533912/1295029"
    ],
    [
      "833477272224325889494472603/14280841",
      "8715676621941224163393125179114883750877/53967298139"
    ]
  ],
  "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 rank13 at T=172128/135161 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 thirteen displayed points and bounds[13,13]. Every coordinate was checked exactly on the minimal model; independence modulo torsion was separately certified by an exact rank-13 F_5 reduction matrix at thirteen good primes.",
  "created_at": "2026-10-29 02:15:36",
  "updated_at": "2026-10-29 02:15:36"
}