{
  "id": 6110,
  "curve_key": "90668057331039764815226545692175398191705641:-469991830496048235241732751975489971541485663116839254885854063061",
  "ainvs": [
    "1",
    "0",
    "1",
    "-1888917861063328433650553035253654128993868",
    "543972026037092864862959201260987745247989378817477999755285306"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 303.6473370644105,
  "faltings_height": 23.351123058213815,
  "conductor": "11643434205218962024218516421340879789523637819129098777570",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "29",
    "31",
    "37",
    "61",
    "67",
    "71",
    "79",
    "109",
    "137",
    "181",
    "193",
    "197",
    "199",
    "229",
    "271",
    "307",
    "677",
    "691",
    "1009",
    "2609",
    "6389",
    "113489"
  ],
  "discriminant": "303508259101253649720879892876525517385597748152059781777716368919527946782382308003112084401392329176208262783052057287656250000",
  "regulator": "65883103304984.71342619944290100036285668336141201929900426066420",
  "points": [
    [
      "-1375421292231678134940",
      "23238550887834679965494877546382"
    ],
    [
      "-1242902089945667884740",
      "31171619593391155565012022785182"
    ],
    [
      "-497141567599086933915",
      "36880390511389301564203995212107"
    ],
    [
      "15367701007650932475885",
      "1897589977655633447261713616268307"
    ],
    [
      "28061037498070114314357",
      "4695041250960773984403552581731279"
    ],
    [
      "-124575592951377234442931757315/406264336",
      "270889107048358347945466667368543270022348087/8188663956416"
    ],
    [
      "-103022698039446143737275/169",
      "84203387691488762495928281367822079/2197"
    ],
    [
      "331578540700477633840/9",
      "588098433344859918553018959885539/27"
    ],
    [
      "176203850820853017558102/121",
      "39514423084761983275167521522274173/1331"
    ],
    [
      "1122875097459411203570580/49",
      "1187748625113672079868765692711166626/343"
    ],
    [
      "2021528377733646059781160/81",
      "2869907183238769949660624557489896553/729"
    ],
    [
      "976563410149059737343990171465/44182609",
      "963208779392991718109802995055923669665735061/293681802023"
    ],
    [
      "62264927250370395814449398491965/1298016784",
      "491120396064210623310723684044554487142953927389/46764948693952"
    ]
  ],
  "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=113489/74391 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 submission 7e9f6673-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 02:32:57",
  "updated_at": "2026-10-29 02:32:57"
}