{
  "id": 6094,
  "curve_key": "945551735610374572308607920613978729417225:-831908279495391810491260435565861217094414603059105797870417125",
  "ainvs": [
    "1",
    "0",
    "1",
    "-19698994491882803589762665012791223529526",
    "962856804971518299178057995326904693560129272196973182611448"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 289.9577616932874,
  "faltings_height": 22.134511925291047,
  "conductor": "25297518055926931121987512801766887116408932913900450",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "23",
    "37",
    "43",
    "79",
    "107",
    "109",
    "149",
    "223",
    "653",
    "719",
    "1567",
    "2083",
    "2857",
    "3719",
    "50383",
    "113539"
  ],
  "discriminant": "88724678104095664145449528930961189523406811635351857989659359051289720704905717605738595479527388007257188560349506250000",
  "regulator": "59907429792130.34519496728688669902332119842546759181126695131137",
  "points": [
    [
      "41074468147329062797",
      "472258730504714428034689156601"
    ],
    [
      "737920494842267247862",
      "19703906846106647496847650031556"
    ],
    [
      "-904998812287278735431053148/11978521",
      "58920890472294434788602243430795661261536/41457661181"
    ],
    [
      "-197142810043642732097552/2209",
      "147197635242562628681471438972438248/103823"
    ],
    [
      "-55967887156324823291987/529",
      "16605755523526031320876156055633767/12167"
    ],
    [
      "355393161216981872008/9",
      "13406654055894586281267172079512/27"
    ],
    [
      "25309975443224983352623/484",
      "2930263779062245407175172750196323/10648"
    ],
    [
      "55307792112593068842298/529",
      "2613859036338549966407277453084127/12167"
    ],
    [
      "240166285738040772388933/8464",
      "508682439139234671586405805474272363/778688"
    ],
    [
      "2355504027296051119791232/3481",
      "3542263700241025973748777246151979029/205379"
    ],
    [
      "30825628084124178491864332/36481",
      "168907402858021564736304261703141695421/6967871"
    ],
    [
      "34581993801022948499965888/277729",
      "97149217698693634830357598935083132233/146363183"
    ],
    [
      "47882163339110176627489533913/1145687104",
      "17879231159775024786711509609371274624747167/38779217096192"
    ]
  ],
  "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=151149/77071 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 02:19:09",
  "updated_at": "2026-10-29 02:19:09"
}