{
  "id": 5541,
  "curve_key": "-10082286900285009107914944:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "210047643755937689748228",
    "0"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 172.71846703138903,
  "faltings_height": 12.461445997590577,
  "conductor": "58014480798713096047867061716102842721931808",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "19",
    "23",
    "53",
    "113",
    "131",
    "139",
    "277",
    "307",
    "1217"
  ],
  "discriminant": "-593107500740673057928287900688637236692634518432664087309771540988694528",
  "regulator": "44091382285407525822.5612405127584824525443392493425909645813",
  "points": [
    [
      "78592819886382088831586575810076944/2329176576344708905378729",
      "300072802823052489392700189230151543706814950502896264/3554705456827670123842692043652328683"
    ],
    [
      "18370430004673148923288725885770896/33296445843768523057041",
      "3236887531455436446897576701716224589880337611026792/6075706934751213419924797108927161"
    ],
    [
      "198698943234867753738464713559056/506101332491184721225",
      "-4305246594193318116987254040412055994044366420296/11385607839962651990435037842875"
    ],
    [
      "19607615891048711172428568890944/7186557361823515225",
      "88039904894812343187218762546226219888823826128/19265547012719475366409715875"
    ],
    [
      "1439217842108699477625725014379584/654525713416277422801",
      "-55773016286132563096853895336528237213969366402416/16745189593161399427571834542951"
    ],
    [
      "516745393912577487513458657218234742318656/915254174367491245305111176281",
      "478443532071282355437167337340727195621578151787506132193948208/875613759462778976770418369374662836696841821"
    ],
    [
      "47181426739715012441276845812121/302221076401094131264",
      "1005095573280098486633573031158756899630114164803/5253964355380371841190347545088"
    ],
    [
      "22460016658898702861760664460219722293849360845307904/141984305399301485104764095369175313128025",
      "10316789781963980143879348984833035766194893013204971402185214680538303522913792/53500829032298263422459144386711098459075854553349338821260125"
    ],
    [
      "14694073715862836483256389526463447326262904689/62419008050062093459624182723216",
      "1781205979566511640079003378110740104766004771295319523494541185701239/493145749244961155350830168133569214670902700736"
    ],
    [
      "20903212374941229570646218449896138703768648070271729/65729236996583224745401174939206950194576",
      "-5301197614391242179112729258279081121584875872176719370542382873025874156178999/16851473677889555555766091502026245879363013855194693369002176"
    ],
    [
      "5509425276897413794525075260376223545551801159166401951197209/60055319929039012809673231457294953766221095054400",
      "-65886174941384552699117105292268866043874074848173308206910771020106613265857347529863703677/465400909169648501108297219486473541383983978718820929818240738255988928000"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of my ICARM curve #5504:\r\nhttps://elliptic-rank.icarm.cloud/curve/5504\r\n\r\nCurve #5504 was obtained from a curve from my own run at tuple (11,23,29,50), capture APH-07f1610bc9cb7d3079b579ba. Its model is y^2 = x^3 - 52511910938984422437057*x. Applying the rational 2-isogeny (x,y) -> (x + A/x, y*(1 - A/x^2)) with A = -52511910938984422437057 gives the submitted model y^2 = x^3 + 210047643755937689748228*x.\r\n\r\nThe 11 submitted points are the exact transported images of the 11 witnesses on #5504; every image was checked exactly on the target. Rational isogeny preserves rank and conductor. The conductor is 58014480798713096047867061716102842721931808. This completes the rational 2-isogeny pair from the same own-run tuple capture.",
  "created_at": "2026-10-22 23:56:19",
  "updated_at": "2026-10-22 23:56:19"
}