{
  "id": 3401,
  "curve_key": "349162935310661697:-206320415507349018542561889",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-7274227818972119",
    "238796779026136837315439"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    9
  ],
  "naive_height": 121.18294521465148,
  "faltings_height": 7.469281257084459,
  "conductor": "8825955642",
  "bad_primes": [
    "2",
    "3",
    "7",
    "29",
    "271",
    "2971"
  ],
  "discriminant": "-2205063300352431019556068635503699951616",
  "regulator": "223.316026026613326353416951300563404264975",
  "points": [
    [
      "2956298820771/60025",
      "1327690654567334/14706125"
    ],
    [
      "1882819419564257569/38310624361",
      "8519756602516706218374014/7498576816802891"
    ]
  ],
  "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 = 1/29; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 8825955642, torsion ℤ/9ℤ.",
  "created_at": "2026-09-26 21:21:13",
  "updated_at": "2026-09-26 21:21:13"
}