{
  "id": 3368,
  "curve_key": "33841761409:-6751397899995841",
  "ainvs": [
    "1",
    "0",
    "0",
    "-705036696",
    "7814059186752"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    7
  ],
  "naive_height": 72.89705194929866,
  "faltings_height": 4.035042106313868,
  "conductor": "9096906",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "16661"
  ],
  "discriminant": "-3948839685064974266724777984",
  "regulator": "8.43938008405163067603977566220661834158270",
  "points": [
    [
      "2352",
      "2482536"
    ],
    [
      "128037/16",
      "104606229/64"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/7ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with b=t^3-t^2, c=t^2-t, at t = 8/21; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 9096906, torsion ℤ/7ℤ.",
  "created_at": "2026-09-26 21:13:42",
  "updated_at": "2026-09-26 21:13:42"
}