{
  "id": 2018,
  "curve_key": "2598178093391939718106923369936155200:-4187968196968760668931384232146801989533217134183232000",
  "ainvs": [
    "0",
    "1",
    "0",
    "-54128710278998744127227570207003233",
    "4847185413158287793220272768281439445476477910377663"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2
  ],
  "naive_height": 251.54362144162184,
  "faltings_height": 18.144840099930647,
  "conductor": "207871256848409744593342350561253204800",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "23",
    "37",
    "41",
    "101",
    "359",
    "389",
    "541",
    "12479",
    "23209",
    "49411",
    "51431"
  ],
  "discriminant": "795583344544664764303972590235535004991119606275080777471224142334339890146425507328000000",
  "regulator": "713821792862775.422994149722046305923863662939091079029923555",
  "points": [
    [
      "4868973444785824535153717/35844169",
      "-206550525072816456214673002499522100/214599039803"
    ],
    [
      "134323878404684018",
      "-2041280717927396475"
    ],
    [
      "2149339585262040113/16",
      "400140940747689199318575/64"
    ],
    [
      "5498468389022631735772397/40934404",
      "2508012418119231452873031984675/261898316792"
    ],
    [
      "1293667419253484178003818/9628609",
      "-621190094584126008982740106550481/29877573727"
    ],
    [
      "1114266841967821912133/8281",
      "-111570338305073504312487947700/753571"
    ],
    [
      "3612730934593397954085422018/26895672001",
      "-4562246263252210283236297549974525/4410863312491999"
    ],
    [
      "36042324028604108502421/268324",
      "1498825690960309066269433233/138991832"
    ],
    [
      "36461009678795314490057/271441",
      "-888615224740377916660936008/141420761"
    ],
    [
      "26999258958885200497137748757/436057924",
      "4436338794849194339629120917630358665849825/9105761568968"
    ],
    [
      "35826975529390057093111605925319522/6291023572936729",
      "-6775763086934290915979407848527009446471276346756625/498978655853413128072317"
    ]
  ],
  "submitter": "Steps Unbounded",
  "history": [],
  "commentary": "Obtained by quotienting the rank-11 Z/2Z x Z/2Z curve of Dujella–Peral by the rational 2-torsion point with x-coordinate -67161937901586997. The 11 displayed points are the exact images of their independent rank-11 generators under the rational 2-isogeny.",
  "created_at": "2026-09-26 05:01:12",
  "updated_at": "2026-09-26 05:01:12"
}