{
  "id": 6117,
  "curve_key": "1117476067184804176981208773037077824:-302495073824452553790803902846388918790864978285445632",
  "ainvs": [
    "0",
    "0",
    "0",
    "-23280751399683420353775182771605788",
    "350110039148671937257874887553690878230167798941488"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 249.01240793601738,
  "faltings_height": 18.815165357887068,
  "conductor": "772192493487310998102753440165321757670062546240",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "31",
    "41",
    "61",
    "79",
    "139",
    "163",
    "167",
    "239",
    "367",
    "631",
    "859",
    "1187",
    "3023",
    "13669",
    "450581"
  ],
  "discriminant": "754599568437256440244802210052934105190239366053401697942121348021049334692267619007184512711273791897600",
  "regulator": "231048397058686.08261959454376151617385981153594305038635949099",
  "points": [
    [
      "-112851328137825516",
      "39244928818047105040864200"
    ],
    [
      "-12740424549514376",
      "25389932852581799238254980"
    ],
    [
      "151185166820585029",
      "16912665648992678991832945"
    ],
    [
      "363220289977138341",
      "199532831364138651426496449"
    ],
    [
      "3264209965306974409/16",
      "4093916324464581772322751355/64"
    ],
    [
      "2785295997381960985186/18769",
      "32863121684021594671754176651600/2571353"
    ],
    [
      "3772778614241820013578/24649",
      "74695511608569822184349557284720/3869893"
    ],
    [
      "853618526346265305588996/1079521",
      "774133626820217280840618091049008656/1121622319"
    ],
    [
      "1882598531250070398647608/4338889",
      "2423994897473480259678624934898418580/9037905787"
    ],
    [
      "121501013459882825041161636/330257929",
      "1223825818044980772314155484707511826000/6001777343717"
    ],
    [
      "174317430710188571442732381/1160151721",
      "617584570499666399891517549216260694819/39515927768981"
    ],
    [
      "15980565284133840319207552283533046870644/103392927689817083610681",
      "700658834174896390853785918325888992436673925226203217977880/33245758788590148526704984927758829"
    ]
  ],
  "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=-9317/6046 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 03:01:06",
  "updated_at": "2026-10-29 03:01:06"
}