{
  "id": 4298,
  "curve_key": "26182855927638798830012725168:-4230370930431778120155337257111496436604160",
  "ainvs": [
    "0",
    "1",
    "0",
    "-545476165159141642291931774",
    "4896262650962524332198809518887171713256"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 196.30470706054925,
  "faltings_height": 14.146900713119916,
  "conductor": "81227180467392566378365208705376",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "17",
    "31",
    "43",
    "89",
    "97",
    "167",
    "683",
    "733",
    "1031",
    "12611",
    "27823"
  ],
  "discriminant": "30907266709720414267190667657062061801689969180627815432267126636683017109332544",
  "regulator": "842224904703867.7964698149276723567353180606186645036437862",
  "points": [
    [
      "48549460337355722374/1755625",
      "243522431625935448473734315068/2326203125"
    ],
    [
      "2420772274936095682606/15062161",
      "-117911906298516955408759368046368/58456246841"
    ],
    [
      "16459190120717334214/243049",
      "-63236168590652891886217048884/119823157"
    ],
    [
      "38205792468637311698134/2739161569",
      "-175465561894271781341402229906636/143359499036753"
    ],
    [
      "41787055350251809780100100349/2973950830059364",
      "-393120358601791887928174479648947840982141/162181262077309212932888"
    ],
    [
      "7325724437040111834824086/504305921025",
      "2200694521640652075390984859359455884/358130328286298625"
    ],
    [
      "27628830325427408582431591297777/1408749964281383824",
      "69785912759049123580189085533297248352375498545/1672056225060298284365327168"
    ],
    [
      "84955933716754684845340366/5941898635201",
      "64789637056327572668109341635015924032/14483978055064592801"
    ],
    [
      "45571547602955774589000279018837073/1077558807427585647376",
      "8479617968235286422358673668473311427606418399808385/35372151092732853008602604541376"
    ],
    [
      "7820667691245255193421395450060077841/53074828564999201960000",
      "-21611323032394510234549471360505763121338158189794862361/12227365661792614906745427256000000"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve#4251, submitted by Michael Rubinstein. The source is a specialization at t = -167/1118 of the Elkies-Klagsbrun Z/4 fibration E2. This isogenous curve has the same rank and conductor, with torsion subgroup Z/2 x Z/2. The ten supplied points were transported from the source curve.",
  "created_at": "2026-10-16 19:04:50",
  "updated_at": "2026-10-16 19:04:50"
}