{
  "id": 3400,
  "curve_key": "6012890251873:-14744325694797569809",
  "ainvs": [
    "1",
    "0",
    "0",
    "-125268546914",
    "17065181337340500"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    8
  ],
  "naive_height": 88.2747799680315,
  "faltings_height": 4.70363482985748,
  "conductor": "16824234",
  "bad_primes": [
    "2",
    "3",
    "7",
    "19",
    "29",
    "727"
  ],
  "discriminant": "2617227016901882338755312",
  "regulator": "40.1069051925038460665734191783063743132247",
  "points": [
    [
      "1146607/4",
      "547930061/8"
    ],
    [
      "377903428/1849",
      "-5673105410/79507"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/8ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with b=(2t-1)(t-1), c=b/t, at t = 1/58; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 16824234, torsion ℤ/8ℤ.",
  "created_at": "2026-09-26 21:21:03",
  "updated_at": "2026-09-26 21:21:03"
}