{
  "id": 3676,
  "curve_key": "25777380142287902973542976:-130511583822350163511615860964116619776",
  "ainvs": [
    "0",
    "0",
    "0",
    "-537028752964331311948812",
    "151055073868460837397703542782542384"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    4
  ],
  "naive_height": 175.53461880166057,
  "faltings_height": 12.44009048259803,
  "conductor": "3407621442773364069580883520",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "23",
    "37",
    "59",
    "73",
    "83",
    "89",
    "139",
    "167",
    "239",
    "563",
    "823"
  ],
  "discriminant": "55039370759216222062338862745364840640400890755879789029736000000000000",
  "regulator": "223974110.13773635322004743744432487555207066747301791124",
  "points": [
    [
      "447579071448",
      "18826237010688700"
    ],
    [
      "503121301598",
      "90664706886687000"
    ],
    [
      "1521668968238",
      "1690344268013428920"
    ],
    [
      "-814605474826732/326041",
      "72676878353797636001250000/186169411"
    ],
    [
      "-64794036682562/81",
      "191186944644854969000/729"
    ],
    [
      "3640928700382/9",
      "81618793971247000/27"
    ],
    [
      "6986556537757/9",
      "12134093760438473125/27"
    ],
    [
      "28398199536705/64",
      "5785145736133910431/512"
    ],
    [
      "4483512050491892/16129",
      "312354258014147599980000/2048383"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 961/1280 of the Elkies-Klagsbrun Z/4 fibration E1: y^2 + a*xy + a*c*y = x^3 + c*x^2, a = (8t-1)(32t+7), c = 8(t+1)(15t-8)(31t-7) (arXiv:2003.00077, eq. (5)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:31:19",
  "updated_at": "2026-09-29 19:31:19"
}