{
  "id": 3650,
  "curve_key": "174495948442333021774560068027323201:-72844954628808902220692073149389266302558398035956449",
  "ainvs": [
    "1",
    "0",
    "0",
    "-3635332259215271286970001417235900",
    "84311290079639932822856655654964969491572101846032"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 243.4416287762428,
  "faltings_height": 18.04425122398101,
  "conductor": "216095858582728308893742177217643607485136038653170",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "29",
    "31",
    "37",
    "67",
    "79",
    "139",
    "157",
    "211",
    "241",
    "257",
    "509",
    "709",
    "2801",
    "12301",
    "16529",
    "50263",
    "53617"
  ],
  "discriminant": "3941612203978209437354651320619679980678243786566130660883873496471712063994279661674898329600000000",
  "regulator": "1758684180088111.3300535324698546066450750364767343833781353746552823",
  "points": [
    [
      "-65190603024930516",
      "6652278419230975966040928"
    ],
    [
      "23998194782033304",
      "3300115022899654561593348"
    ],
    [
      "29391200688944304",
      "1689344115135726282966348"
    ],
    [
      "29420146807628304",
      "1680399762414432386073348"
    ],
    [
      "31584462345719304",
      "999624046964685922239348"
    ],
    [
      "144357933635405091/4",
      "2757434274236009285496159/8"
    ],
    [
      "466441332170465904",
      "316023929611923409666002948"
    ],
    [
      "515111910532102904",
      "367275981952250591129542148"
    ],
    [
      "2600084813769317091/4",
      "4175150443397367506982967659/8"
    ],
    [
      "-168978512601106805481864/8720209",
      "312720578507529989260084017473367396/25750777177"
    ],
    [
      "-485147613487664876/81",
      "7500916281543350892163020692/729"
    ],
    [
      "148044979510031128/9",
      "145306817181490729468338796/27"
    ],
    [
      "19068116877419614392/529",
      "3981274245413000608702763292/12167"
    ],
    [
      "3899823088292135073111/77284",
      "116411993534498724577730306654871/21484952"
    ],
    [
      "77445206462484645004584/19321",
      "21549785865935750076883820403644412/2685619"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -512/1427, u = 2/5 of the Elkies-Klagsbrun family y^2 = x^3 + 2A(t,u)x^2 + B(t,u)x (arXiv:2003.00077, Sec. 9, eqs. (3)-(4)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:26:57",
  "updated_at": "2026-09-29 19:26:57"
}