{
  "id": 6086,
  "curve_key": "152227143815677978506437742932495376:-59223361037102129032575708579633104539770941282813376",
  "ainvs": [
    "0",
    "0",
    "0",
    "-3171398829493291218884119644426987",
    "68545556755905241935851514559760537661771922781034"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 243.03204552420792,
  "faltings_height": 18.06603102518223,
  "conductor": "92611563353346759675602332566666653471281680",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "73",
    "79",
    "97",
    "101",
    "103",
    "139",
    "181",
    "421",
    "653",
    "787",
    "997",
    "2411",
    "6701",
    "35977"
  ],
  "discriminant": "11671781451031797846610595194896594637987255180957280851880721496502288073746867680324667590416000000",
  "regulator": "159117457690104.3607529419577446782663739375717093178538101180977",
  "points": [
    [
      "-16527058670996727",
      "10790977242503344027125600"
    ],
    [
      "9230889189739273",
      "6329082345114138804706400"
    ],
    [
      "11489692092246673",
      "5798616188845976588825200"
    ],
    [
      "25510236286260873",
      "2060042404865798554185600"
    ],
    [
      "-549164792189608119/64",
      "4993682621381853180877629765/512"
    ],
    [
      "-296346649628216789/9",
      "316339467665220708519841030/27"
    ],
    [
      "7143065933055940297/64",
      "17018915098261338601513013125/512"
    ],
    [
      "312335970282966443562/18769",
      "11607730160392309957231305537450/2571353"
    ],
    [
      "4257936047142321784443/1042441",
      "7940508141645412873233900439983750/1064332261"
    ],
    [
      "65368191182038684896873/2105401",
      "299383488583138702922235743887200/3054936851"
    ],
    [
      "194753448105092269361577/6285049",
      "2590088811016058025360228045504000/15756617843"
    ],
    [
      "1049927048295307778605947/2053489",
      "1069549617483448002999415874477171250/2942649737"
    ],
    [
      "17683679417556431593229307/515153809",
      "4214523619964265618715873497461711250/11692446002873"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Original specialization/search by 0xArion (2026), public Yukon elliptic-rank challenge submission e4015be6-ebb5-475f-b505-f1b867f7cc35. Source: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/c1890e67b75e1de012b04c7add6c860ec2ba495e/submission/board/2x2-13-p724-q10981.ec . Specialization T=724/10981 of 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 thirteen supplied points have been checked exactly on the minimal model and certified independent modulo torsion by an exact rank-13 F_7 reduction matrix at thirteen good primes.",
  "created_at": "2026-10-29 01:13:35",
  "updated_at": "2026-10-29 01:13:35"
}