{
  "id": 3667,
  "curve_key": "4609175088452862669201:-312871877537869902326198095503801",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-96024481009434638942",
    "362120228655799988685458307309"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    4
  ],
  "naive_height": 149.64700756282153,
  "faltings_height": 10.180587549401826,
  "conductor": "2542465729285305792210",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "31",
    "37",
    "43",
    "103",
    "389",
    "487",
    "140449"
  ],
  "discriminant": "17815595092280169081648964232294920753115884408704860160000",
  "regulator": "137200.343000733322394238313457040513446342359688666981",
  "points": [
    [
      "-7938235783",
      "790037265530691"
    ],
    [
      "5065687457",
      "75375082920051"
    ],
    [
      "5543816669",
      "12695077276587"
    ],
    [
      "5592123257",
      "3933317725251"
    ],
    [
      "27037665089",
      "4187029708157067"
    ],
    [
      "34998349689",
      "6314280344267843"
    ],
    [
      "-110641817047/49",
      "258375402074895813/343"
    ],
    [
      "1486947843993/289",
      "320849338232201683/4913"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 389/90 of the Elkies-Klagsbrun Z/4 fibration E2: y^2 + a*xy + a*c*y = x^3 + c*x^2, a = -8(80t+9), c = 2(t-2)(2t-1)(18t-1)(2t-81) (arXiv:2003.00077, eq. (6)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:29:48",
  "updated_at": "2026-09-29 19:29:48"
}