{
  "id": 6097,
  "curve_key": "6971422557861008366968353037330630517732800:-11050302143828559494473049632410789941628442652362241213192320000",
  "ainvs": [
    "0",
    "1",
    "0",
    "-145237969955437674311840688277721469119433",
    "12789701555357129044480579973453268392854898766363723877414263"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 295.9511796208543,
  "faltings_height": 22.70415854915197,
  "conductor": "60683857455542064605589057157930052320159888388875200",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "23",
    "37",
    "43",
    "67",
    "71",
    "101",
    "103",
    "127",
    "139",
    "149",
    "191",
    "199",
    "227",
    "379",
    "643",
    "1231",
    "2179",
    "4327",
    "4373"
  ],
  "discriminant": "125409181291379724073823552163902947202768908046737111671588808487447865375573062674336797964794785955000400345453675584000000",
  "regulator": "21962198993247.45155513198861912112581408627860334812425233884906",
  "points": [
    [
      "-254071943519929949217",
      "5769714237814869019999132026600"
    ],
    [
      "52886569926345268443",
      "2292702918045204158324157373200"
    ],
    [
      "383793968991632781282",
      "3685139886762435736715271082857"
    ],
    [
      "660934924541230601823",
      "14335841298512574030143172403800"
    ],
    [
      "1108794490879985465193",
      "34855853953387950739107118875300"
    ],
    [
      "293813169214827575965443",
      "159259930312251482516488174535554200"
    ],
    [
      "-157860573722339828099053522107/644093641",
      "94842895354054507422130713120832926649487400/16346452514939"
    ],
    [
      "-70433589815477041447857387/177241",
      "207740436918461251616317556647295483400/74618461"
    ],
    [
      "56313457557213872085631/729",
      "28053458877456145659720932202912832/19683"
    ],
    [
      "4715599913622357740819296557/4592449",
      "302744793157575252518064960864276037819200/9841618207"
    ],
    [
      "46056732521301541324776867167/140968129",
      "772680872093554370056882447476795131537400/1673714595617"
    ],
    [
      "98977043355759078089188071507/13126129",
      "31099458258345961749003243226710638088562200/47555965367"
    ],
    [
      "2017727488384615982269844581659/60226558921",
      "41704175198040061983630411941263134017352486936/14780260051361531"
    ]
  ],
  "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=-14707/17361 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_7 reduction matrix at thirteen good primes.",
  "created_at": "2026-10-29 02:26:33",
  "updated_at": "2026-10-29 02:26:33"
}