{
  "id": 2163,
  "curve_key": "806013051726826693949536:-13892813560657011534320424159550977760",
  "ainvs": [
    "0",
    "1",
    "0",
    "-16791938577642222790615",
    "16079645324828906777789424999290834"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 171.0488700884037,
  "faltings_height": 12.311895883781428,
  "conductor": "294986299695893757693379720933488412787544",
  "bad_primes": [
    "2",
    "3",
    "7",
    "37",
    "41",
    "43",
    "61",
    "127",
    "163",
    "179",
    "199",
    "239",
    "277",
    "283",
    "607",
    "1097",
    "17047"
  ],
  "discriminant": "-111392729501243415563031633154958510364231521565006537693848946846144048",
  "regulator": "320211954562.8368943751026307523407535705714208888155086070329944",
  "points": [
    [
      "168020285887",
      "134170074377566899"
    ],
    [
      "2896191488165/4",
      "4954191353809735401/8"
    ],
    [
      "-8741671424599/400",
      "1025629381211328462051/8000"
    ],
    [
      "1148629390931",
      "1229729855762202711"
    ],
    [
      "5283524307029/4",
      "12128580805775893137/8"
    ],
    [
      "-273750603085",
      "12717888738012297"
    ],
    [
      "310777949666",
      "202180432494494436"
    ],
    [
      "89201552289286/81",
      "841716828366538143194/729"
    ],
    [
      "246423418310",
      "164029441121687778"
    ],
    [
      "-1196793476345434/9409",
      "116012226751373826545814/912673"
    ],
    [
      "-34211591727223/256",
      "517086413332365290661/4096"
    ],
    [
      "343183489382",
      "225245050840646214"
    ],
    [
      "96130729442",
      "123910368220115484"
    ]
  ],
  "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=-9/13 (the 2-isogenous partner of that fibre); one of the smallest fibres of the family (|a|,b<=40 over 8 values of u), rank certified with PARI ellrank: 13 independent points.",
  "created_at": "2026-09-26 14:17:28",
  "updated_at": "2026-09-26 14:17:28"
}