{
  "id": 2146,
  "curve_key": "48884958009234052493791051671785901877761:-5084938593874354577682726745899241381379684469508943420497665",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1018436625192376093620646909828872955787",
    "5885345594761984465165172519607401177779796530129606457115"
  ],
  "rank_lower_bound": 17,
  "torsion": [
    2
  ],
  "naive_height": 281.0708651062641,
  "faltings_height": 21.475762102552093,
  "conductor": "18331238590268621233314106535710120397922860155863660882325091066952394194",
  "bad_primes": [
    "2",
    "3",
    "43",
    "59",
    "71",
    "83",
    "151",
    "157",
    "163",
    "233",
    "331",
    "503",
    "617",
    "1061",
    "1097",
    "9109",
    "43607",
    "45589",
    "53831",
    "290761",
    "6923687",
    "322437920267"
  ],
  "discriminant": "52642185190662835903453865489574151738698284302595303449862441182888582893882932003889202077851991627389985755557527552",
  "regulator": "2275832272073902918.66612151415823533442318522418412636015247694194888698",
  "points": [
    [
      "4701737782536591947",
      "34653453511120231760510654922"
    ],
    [
      "-7021755092120972053",
      "112651454525439849773192525130"
    ],
    [
      "-20849226553494100777",
      "134372638836755647806121445274"
    ],
    [
      "265629708239995233859/9",
      "1058457510596232042484056785102/27"
    ],
    [
      "75692414394446704907",
      "602050759353034087042701371850"
    ],
    [
      "-3897672949780489701997/121",
      "96598652467233178188612595252542/1331"
    ],
    [
      "-31118773598535966763",
      "86273439913626203893149981510"
    ],
    [
      "-204630933877381575493/49",
      "34412402987253183723668447893926/343"
    ],
    [
      "411967444066420099883",
      "8336922297560136964928309004042"
    ],
    [
      "21860327056733272260899/4489",
      "9705344175855551710375757913420078/300763"
    ],
    [
      "11766656342725593354785155/335241",
      "22451907647285139900039162067491320846/194104539"
    ],
    [
      "-23468068566190202773",
      "129850073934152050084986322890"
    ],
    [
      "-361419812915535488497129/14161",
      "208124801578607559760670474494824114/1685159"
    ],
    [
      "-34005199517294844117",
      "34575302567553096730668428042"
    ],
    [
      "79109635355087743891451/49",
      "22246388494640512817767553307148710/343"
    ],
    [
      "4807668545457161595",
      "33168701561131947567501440954"
    ],
    [
      "42023788095174738737099735/1471369",
      "17476160475442088811750983132170755678/1784770597"
    ]
  ],
  "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=74/4903. Found by a Mestre-Nagao sieve over t=a/b with |a|,b<=30000, screened with PARI ellrank (2-descent): 17 independent points, 2-Selmer upper bound 17.",
  "created_at": "2026-09-26 11:54:47",
  "updated_at": "2026-09-26 11:54:47"
}