{
  "id": 3370,
  "curve_key": "796909767145441:-33301812447304046951761",
  "ainvs": [
    "1",
    "0",
    "0",
    "-16602286815530",
    "38543763023078004900"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    7
  ],
  "naive_height": 103.71979755245437,
  "faltings_height": 6.671606390840471,
  "conductor": "24896975610",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "79",
    "808081"
  ],
  "discriminant": "-348912656234165824852274138454589440000000",
  "regulator": "182.32108503701838749132267507262071579342474",
  "points": [
    [
      "-1404325260/289",
      "10410720921510/4913"
    ],
    [
      "580132540/49",
      "13289137029610/343"
    ],
    [
      "25900409860/3721",
      "3660739552339870/226981"
    ]
  ],
  "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 = 79/40; converted to the global minimal model. The 3 witness points were found with PARI/GP ellrank. Conductor 24896975610, torsion ℤ/7ℤ.",
  "created_at": "2026-09-26 21:16:09",
  "updated_at": "2026-09-26 21:16:09"
}