{
  "id": 3638,
  "curve_key": "1276053467327626092460201:-1626930695154554001464352471075514645",
  "ainvs": [
    "1",
    "0",
    "1",
    "-26584447235992210259588",
    "1883021637908148057017778972149102"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 166.75951715681268,
  "faltings_height": 11.875571863738402,
  "conductor": "551664926630833203374698683114972985506",
  "bad_primes": [
    "2",
    "3",
    "11",
    "23",
    "47",
    "53",
    "59",
    "89",
    "157",
    "251",
    "317",
    "521",
    "7607",
    "9533",
    "55997",
    "95569"
  ],
  "discriminant": "-329334338676931735094752960766191284170572391342767104152001882159708",
  "regulator": "6963504929908.204124646260172139829621030678306948989635030177765",
  "points": [
    [
      "-183830241354",
      "23617228343695558"
    ],
    [
      "-164268709683",
      "42630508966552441"
    ],
    [
      "-27740385429",
      "50981750012106133"
    ],
    [
      "601674726",
      "43209103667138278"
    ],
    [
      "23241539760",
      "35745093131163493"
    ],
    [
      "25080144429",
      "35100637236226177"
    ],
    [
      "62530420215",
      "21568053176674081"
    ],
    [
      "-124140812528490/5041",
      "17976836370414805133573/357911"
    ],
    [
      "838667783619/49",
      "12984370708861759339/343"
    ],
    [
      "214961515825449/256",
      "3096789656852165404867/4096"
    ],
    [
      "1486146486122229/784",
      "57087395558460140154721/21952"
    ],
    [
      "519209165870076/961",
      "11353025978269864997758/29791"
    ],
    [
      "3043703389005759/44521",
      "184343767087289987445037/9393931"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = 54/47 of the rank-9 fibration of X400, y^2 + (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #802 (same T), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:24:34",
  "updated_at": "2026-09-29 19:24:34"
}