{
  "id": 3369,
  "curve_key": "140112991681:-52570740406453921",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2919020660",
    "60845521107600"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    7
  ],
  "naive_height": 77.001872187688,
  "faltings_height": 4.2225871541725075,
  "conductor": "13422930",
  "bad_primes": [
    "2",
    "3",
    "5",
    "19",
    "23549"
  ],
  "discriminant": "-7542518754050368634880000000",
  "regulator": "10.2195833769297217083158645549767764869076",
  "points": [
    [
      "1538280/49",
      "126308820/343"
    ],
    [
      "5013160/169",
      "1283649340/2197"
    ]
  ],
  "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 = 24/19; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 13422930, torsion ℤ/7ℤ.",
  "created_at": "2026-09-26 21:13:53",
  "updated_at": "2026-09-26 21:13:53"
}