{
  "id": 3683,
  "curve_key": "58541618937423854610458023323456:-447916166652474021596406268118678682334429999104",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1219617061196330304384542152572",
    "518421489181104191662507254766989215664849536"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    4
  ],
  "naive_height": 219.44187217781143,
  "faltings_height": 15.850916019645517,
  "conductor": "27224080399408186552476519408543840",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "19",
    "37",
    "41",
    "43",
    "53",
    "59",
    "73",
    "89",
    "101",
    "283",
    "829",
    "11351",
    "164209"
  ],
  "discriminant": "189779571043628733737782697385637703752705610048948874375235667742510675398961600000000",
  "regulator": "4553739249.700043742967987173966564380993000522648680677736",
  "points": [
    [
      "-817436931196843",
      "31131456689604805313375"
    ],
    [
      "638076902334562",
      "1989966773384330220"
    ],
    [
      "1020756255429536",
      "18359191695107671469840"
    ],
    [
      "1245796219050202",
      "30537078074312839640820"
    ],
    [
      "-6275749059570653758/5041",
      "3706841623222811120004039220/357911"
    ],
    [
      "-46890291040970603/121",
      "40652306924057457033456225/1331"
    ],
    [
      "2802489483902233/4",
      "22408842660996262888035/8"
    ],
    [
      "6702140703875338/49",
      "6454993319800306389256140/343"
    ],
    [
      "611456865544991002/961",
      "1623849081498558916159500/29791"
    ],
    [
      "26402609731261726933/26569",
      "73466124506646865273811656575/4330747"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 918/829 of the Elkies-Klagsbrun Z/4 fibration E2: y^2 + a*xy + a*c*y = x^3 + c*x^2, a = -8(80t+9), c = 2(t-2)(2t-1)(18t-1)(2t-81) (arXiv:2003.00077, eq. (6)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:32:30",
  "updated_at": "2026-09-29 19:32:30"
}