{
  "id": 3374,
  "curve_key": "1633933212919281:-66959056547229387769929",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-34040275269152",
    "77498916550843571651"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    9
  ],
  "naive_height": 105.11673657832092,
  "faltings_height": 6.638303434692201,
  "conductor": "3054566970",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "71",
    "103"
  ],
  "discriminant": "-70221113154273618228597016011264000000000",
  "regulator": "27.7831692355216756542207964105614157421384",
  "points": [
    [
      "-544928819/81",
      "1038948512921/729"
    ],
    [
      "36791732421/11881",
      "1726954254558901/1295029"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/9ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with c=t^2(t-1), b=c(t^2-t+1), at t = 7/20; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 3054566970, torsion ℤ/9ℤ.",
  "created_at": "2026-09-26 21:16:41",
  "updated_at": "2026-09-26 21:16:41"
}