{
  "id": 3399,
  "curve_key": "7211738881:-51651139246721",
  "ainvs": [
    "1",
    "1",
    "1",
    "-150244560",
    "59718809265"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    8
  ],
  "naive_height": 68.09692780634366,
  "faltings_height": 3.7425509079412835,
  "conductor": "9409530",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "23",
    "1049"
  ],
  "discriminant": "215514333746490320100000000",
  "regulator": "13.1564070133689794141150680723178581411636",
  "points": [
    [
      "-1637",
      "549713"
    ],
    [
      "15199",
      "1127105"
    ]
  ],
  "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 = 13/3; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 9409530, torsion ℤ/8ℤ.",
  "created_at": "2026-09-26 21:20:53",
  "updated_at": "2026-09-26 21:20:53"
}