{
  "id": 6128,
  "curve_key": "9279651020920961721905601220630613056:-239523794479592689963206520173933932500385591508923784704",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-193326062935853369206366692096471105",
    "277226613981010057892227345254004285684975924574892897"
  ],
  "rank_lower_bound": 18,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 259.6364955684799,
  "faltings_height": 19.69410203481989,
  "conductor": "1267548066931185496991495042988782951726511449140210157873613120",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "23",
    "29",
    "31",
    "43",
    "53",
    "61",
    "113",
    "127",
    "149",
    "271",
    "373",
    "433",
    "769",
    "827",
    "863",
    "1033",
    "1453",
    "1657",
    "2053",
    "6991"
  ],
  "discriminant": "-32738749726314483519098577760507579917483485715113725033745485280593228446093741552814609460728332605546496000",
  "regulator": "159550392406753899890880658.83534071534382214987383002562103386508713457210",
  "points": [
    [
      "-15956347108569918990531/21316",
      "155300493675335707661084677425465/3112136"
    ],
    [
      "-7718381982982044169133/84681",
      "13363474597714012121944525833363764/24642171"
    ],
    [
      "38013338251026425778875976/101465329",
      "-518520500821815754687204876617326124915/1022060259017"
    ],
    [
      "92786865409177196512",
      "-893768314581545962284366821439"
    ],
    [
      "1771717478958853527",
      "-2344375862950167904396832496"
    ],
    [
      "30530554490753756558503/124609",
      "-21753226148020296067945152033456888/43986977"
    ],
    [
      "67681908070903796931903/34969",
      "17489832070880244516339642826167792/6539203"
    ],
    [
      "9680200480396703703205128/3806401",
      "-29921061661045812538474190151964027995/7426288351"
    ],
    [
      "621661089169200856447189685451/125185054225",
      "488783329489795035835577190274639397528073876/44292349960618375"
    ],
    [
      "143972858326477674115272537998499/340316122580281",
      "-3269138923661414735668528070650580911555155645420/6278035781563224012179"
    ],
    [
      "17796569965681257848765912372815321/1318486687584784",
      "-2373003723798585576027608255940853383979961701772715/47875533195263839450048"
    ],
    [
      "226468233355497003049054975797/17037036676",
      "107720628913208710651367265834139993071999099/2223776249171576"
    ],
    [
      "2616885680714259103382743551/10781707225",
      "553683091700074974499793458428901470925776/1119518569707875"
    ],
    [
      "61783109755595402484564291602919/41545256604721",
      "484869921937955772333810180742404621870031499760/267782485706382093481"
    ],
    [
      "127399426537511011042108286810584/50956968712225",
      "-1428460245807701711882516419029051171645197703027/363751989809877623375"
    ],
    [
      "929896114993377339067507483/1473254689",
      "-36060677782269862351953098598814638759588/56547934727887"
    ],
    [
      "-17461778865254827573227814673997/62251042744489",
      "273192789977352797270638200521177936994470420652/491156556434154329237"
    ],
    [
      "328492226040371378934855536026479/10057403738281",
      "5953193745079677840675253914259858829494387187040/31895456828763804821"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogenous partner of curve#6087. Original specialization/search by kaankolcu (2026), public Yukon elliptic-rank challenge submission ddb44e4a-f316-457b-a3f2-7316d2cc04d4. Source: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/236fa93f21f753f95316d5a2449371577693fbb6/submission/board/2-18-own.ec . Parameter T=30/769 in the rank-nine X808 fibration posted by wgxli with curve#4078: y^2+84(35397T^2-221T+20)xy=x(x+F)(x+G), F=(1139T+115)(1269T-59)(3776T+34)(539T-5), G=8(638T-23)(250T-1)(7811T+499). The eighteen independent source points were transported through the rational degree-2 isogeny and the exact minimal-model change. Their independence on this endpoint is certified by an exact rank-18 F_5 reduction matrix at eighteen good primes.",
  "created_at": "2026-10-29 12:22:58",
  "updated_at": "2026-10-29 12:22:58"
}