{
  "id": 2159,
  "curve_key": "41733233885144698076387552264559634081:-269601968465629182207644198292549759041665388347890511729",
  "ainvs": [
    "1",
    "0",
    "0",
    "-869442372607181209924740672178325710",
    "312039315353737479334542068825037861026717661980383172"
  ],
  "rank_lower_bound": 16,
  "torsion": [
    2
  ],
  "naive_height": 259.8730834045106,
  "faltings_height": 19.045168605655377,
  "conductor": "436526112602665716189006848580942310302569667141197757407610",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "43",
    "107",
    "113",
    "179",
    "193",
    "337",
    "647",
    "911",
    "1153",
    "1301",
    "1303",
    "4339",
    "5087",
    "5419",
    "7873",
    "30431",
    "66089",
    "84751"
  ],
  "discriminant": "11355063526709325849038916734316403461532095374556044261684482877054357859534218510244730543030728000",
  "regulator": "25075641006713157.25113783271085298226369106055236796583518244443233252",
  "points": [
    [
      "538383674910806924",
      "50165775054255444925898"
    ],
    [
      "26441041488903256268/49",
      "-553463077012736148528022906/343"
    ],
    [
      "13581742425546099554/25",
      "-783683328669250154399048018/125"
    ],
    [
      "545056052418721004",
      "8547805355344900163345018"
    ],
    [
      "54993898392253985882/121",
      "138098400473955868338118610770/1331"
    ],
    [
      "278905922207866312616/529",
      "-171217324404837678377876525174/12167"
    ],
    [
      "538460681154121904",
      "148309170205384797687218"
    ],
    [
      "283180197713830304",
      "297554973797809434187897778"
    ],
    [
      "70451046011360544057074/137641",
      "1705394832664134337715191675699528/51064811"
    ],
    [
      "441387485472200528954/841",
      "416900086690607916630934005232/24389"
    ],
    [
      "26379125705400375926/49",
      "-1035874323538116921930436/343"
    ],
    [
      "112590008467042643769704/32761",
      "36512408765445421798913757564129518/5929741"
    ],
    [
      "687813124007374988",
      "-198546758289344993562982294"
    ],
    [
      "-589020799040310586",
      "-787274310063905079961325452"
    ],
    [
      "110013682072007102718564908/204404209",
      "-473294568288278918151943888517345846/2922366976073"
    ],
    [
      "223561313921671574",
      "358941715011215512577681798"
    ]
  ],
  "submitter": "Steps Unbounded",
  "history": [],
  "commentary": "Z/2Z curve from the Elkies-Klagsbrun rank-9 family y^2=x^3+2A(t,u)x^2+B(t,u)x (Elkies-Klagsbrun 2020), fibre u=2/5, t=-688/2887 (the 2-isogenous partner of that fibre). Found by a Mestre-Nagao sieve over t=a/b with |a|,b<=30000, screened with PARI ellrank (2-descent): 16 independent points, 2-Selmer upper bound 16.",
  "created_at": "2026-09-26 14:14:45",
  "updated_at": "2026-09-26 14:14:45"
}