{
  "id": 2164,
  "curve_key": "350829150567061210501363825:-6571053366243797696422638466170858415625",
  "ainvs": [
    "1",
    "1",
    "1",
    "-7308940636813775218778413",
    "7605385840556905645594196188764002531"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 183.36702475890084,
  "faltings_height": 12.927656646153217,
  "conductor": "10598095089074167643269066006409167869829050",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "31",
    "61",
    "73",
    "163",
    "173",
    "193",
    "211",
    "229",
    "997",
    "1163",
    "1723",
    "2269",
    "6959",
    "21871"
  ],
  "discriminant": "979702893705634841894394268859136703815446627633094192709560569856000000",
  "regulator": "169234069161.8668409633249045103498468998524231230172625988050490",
  "points": [
    [
      "1595931177719",
      "75168645319103988"
    ],
    [
      "2197678472855",
      "1468675627887115572"
    ],
    [
      "2268120576215",
      "1641912624722503092"
    ],
    [
      "2613175574615",
      "2519998233000871092"
    ],
    [
      "3775602789655",
      "5816493024170785972"
    ],
    [
      "2483684904215",
      "2184801791379520692"
    ],
    [
      "14275501408435/9",
      "1444858895455190984/27"
    ],
    [
      "8029073059991",
      "21599155816257894708"
    ],
    [
      "5107111528215",
      "10172730488316800692"
    ],
    [
      "-12346788080985/4",
      "6959334482439168131/8"
    ],
    [
      "16443849788815/9",
      "15987145312702978364/27"
    ],
    [
      "566230925693335/361",
      "76520101334572115988/6859"
    ],
    [
      "-1015467311785",
      "3739018131668911092"
    ]
  ],
  "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=1/17, t=-1/4; 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 14:17:31",
  "updated_at": "2026-09-26 14:17:31"
}