{
  "id": 2147,
  "curve_key": "2608574544426935240828186981716114081:-4211691585555894980168242668059449951768606312225039729",
  "ainvs": [
    "1",
    "0",
    "0",
    "-54345303008894484183920562119085710",
    "4874643038837841407702987096549823021442506758855172"
  ],
  "rank_lower_bound": 16,
  "torsion": [
    2
  ],
  "naive_height": 251.5556018050938,
  "faltings_height": 18.698595015375403,
  "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": "7013806420802678404714712479061615866937699447140312900893222294104808977653879297346619153167424000000",
  "regulator": "6268910251678289.312784458177713245565922765138091991458795611108083129",
  "points": [
    [
      "45478878207780424",
      "49971440579345617184014498"
    ],
    [
      "1275205559445004",
      "69320586263369860597166818"
    ],
    [
      "-123704294250576776",
      "98510782241622571851178978"
    ],
    [
      "-72786210091833148676/361",
      "599348816631837996112421054422/6859"
    ],
    [
      "255925313240508838",
      "87913824793374674839678516"
    ],
    [
      "8393884563503825884",
      "-24309651031321869715976770142"
    ],
    [
      "145396458058690714",
      "-6835824561867189037938362"
    ],
    [
      "107060780950075684",
      "16838179394731332667120258"
    ],
    [
      "181676381578797163204/1681",
      "-1118955629690076203339577143182/68921"
    ],
    [
      "167626135474583764",
      "-21794413389730861289808062"
    ],
    [
      "170664161457724744",
      "23888397293679577418699938"
    ],
    [
      "96570325435725084",
      "-22958607641096204241832542"
    ],
    [
      "16588786519327877344/25",
      "-63857238895924499221835180038/125"
    ],
    [
      "705299254679193379156/4489",
      "4406233236889654893959050707214/300763"
    ],
    [
      "-51861404793245582564/529",
      "1170831298903329649876959269486/12167"
    ],
    [
      "-659243594953499729/4",
      "773755245533022244193841509/8"
    ]
  ],
  "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. 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 11:54:50",
  "updated_at": "2026-09-26 11:54:50"
}