{
  "id": 3624,
  "curve_key": "75665940309610316281:-656576754498104084624160591245",
  "ainvs": [
    "1",
    "1",
    "0",
    "-1576373756450214922",
    "759926798530798069794077800"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2
  ],
  "naive_height": 137.31857940968274,
  "faltings_height": 9.250458080880042,
  "conductor": "672519215577201888821790774558",
  "bad_primes": [
    "2",
    "3",
    "11",
    "41",
    "53",
    "61",
    "71",
    "89",
    "103",
    "191",
    "499",
    "1013",
    "5653"
  ],
  "discriminant": "1226727845993834425057233609652398817063367323001819772",
  "regulator": "27477669180.0133225324285649571169600248936365346934505018796",
  "points": [
    [
      "-1421837642",
      "11263734044692"
    ],
    [
      "-1036404363",
      "35783898016732"
    ],
    [
      "408741102754",
      "261318455289453262"
    ],
    [
      "-96556513372113/73441",
      "470921814710516251681/19902511"
    ],
    [
      "-46070557043/144",
      "60640894748153695/1728"
    ],
    [
      "145837229314/169",
      "14273443950074278/2197"
    ],
    [
      "941823615477/1369",
      "51833408920992100/50653"
    ],
    [
      "3191540073454/3721",
      "1414559400681173902/226981"
    ],
    [
      "9855074830156/11881",
      "6219678376863383776/1295029"
    ],
    [
      "12672084477346/3481",
      "42718516724929271936/205379"
    ],
    [
      "54838010696629/70225",
      "42145142761670670103/18609625"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = -26/27 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 19:21:42",
  "updated_at": "2026-09-29 19:21:42"
}