{
  "id": 3680,
  "curve_key": "88413074078611999350787201:-831332447431232787077644842901142120801",
  "ainvs": [
    "1",
    "1",
    "1",
    "-1841939043304416653141400",
    "962190332674270473405156542715290760"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    4
  ],
  "naive_height": 179.23218626214575,
  "faltings_height": 12.406538408474999,
  "conductor": "6830331854767804004039231385",
  "bad_primes": [
    "3",
    "5",
    "11",
    "13",
    "17",
    "31",
    "41",
    "43",
    "73",
    "103",
    "127",
    "443",
    "821",
    "941",
    "10487"
  ],
  "discriminant": "9083650504401309454636693753016112941383274011010328590410400390625",
  "regulator": "199048079.78362623140448314302432250294261996678983104641",
  "points": [
    [
      "778362540508",
      "7971950039278808"
    ],
    [
      "3134693396407/4",
      "973038995992339/8"
    ],
    [
      "783754227058",
      "264405930681308"
    ],
    [
      "783808134683",
      "351763491275058"
    ],
    [
      "795319249883",
      "18060451124210058"
    ],
    [
      "38386941387307/49",
      "76905593334787694/343"
    ],
    [
      "38387790771142/49",
      "66716975171893019/343"
    ],
    [
      "330717851313352/169",
      "4839219081464178651176/2197"
    ],
    [
      "886575038954212/1089",
      "1694144059461122991971/35937"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 254/143 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 19:31:59",
  "updated_at": "2026-09-29 19:31:59"
}