{
  "id": 6116,
  "curve_key": "868585556802270156307854255808464825:-808468113230646162426221563766024558812192566128158125",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-18095532433380628256413630329343017",
    "935726982905840470294972881222500303469371200539641"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 248.25652248189408,
  "faltings_height": 18.470552043805267,
  "conductor": "9378724549861212877270871775515267856122067755550",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "37",
    "73",
    "83",
    "137",
    "157",
    "173",
    "373",
    "479",
    "1613",
    "1621",
    "2467",
    "3359",
    "3847",
    "4831",
    "20407"
  ],
  "discriminant": "969764227858417746459356351832868867356883786256940460036142668182770152846818800667458785477722562500",
  "regulator": "8841041346034.3120044111470963546407136148698836169960707973442",
  "points": [
    [
      "-111137283635712376",
      "39674974660427853156747963"
    ],
    [
      "12906044523379544",
      "26539309398050186993517403"
    ],
    [
      "40423110387746924",
      "16440856591342763440365163"
    ],
    [
      "335442975142049431/4",
      "22603762122076202978832419/8"
    ],
    [
      "181846875212790214249",
      "2452215568032358488616170483463"
    ],
    [
      "1362698571406802029/16",
      "224845945117859187341670217/64"
    ],
    [
      "8323633725744065788/121",
      "5398774054865233913081519729/1331"
    ],
    [
      "121713247191063036934/1681",
      "155666738309308046549235271253/68921"
    ],
    [
      "496719646480440116551/6724",
      "798542808712485994795349775559/551368"
    ],
    [
      "9356379974545171435927/145924",
      "348441744617075130638676345362749/55742968"
    ],
    [
      "4046624022300272078497/54289",
      "12949730349295875138410165099216/12649337"
    ],
    [
      "5560275355385172989321/100489",
      "324654797565460581155251628346384/31855013"
    ]
  ],
  "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=55264/65623 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_7 reduction matrix at twelve good primes.",
  "created_at": "2026-10-29 02:57:31",
  "updated_at": "2026-10-29 02:57:31"
}