{
  "id": 3384,
  "curve_key": "-1998233815749311:100946653914704463758879",
  "ainvs": [
    "1",
    "0",
    "0",
    "41629871161444",
    "-116836401524714977008"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    7
  ],
  "naive_height": 105.93775830223638,
  "faltings_height": 6.940962557433147,
  "conductor": "12751938654",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "19",
    "41",
    "4283"
  ],
  "discriminant": "-10514497359084633769917825294479040209485824",
  "regulator": "285.05987295811494860156595926879788971885726",
  "points": [
    [
      "21888952",
      "106205668132"
    ],
    [
      "400026664/9",
      "8078788794172/27"
    ],
    [
      "15815721304/3025",
      "2597029580767132/166375"
    ]
  ],
  "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 = 104/123; converted to the global minimal model. The 3 witness points were found with PARI/GP ellrank. Conductor 12751938654, torsion ℤ/7ℤ.",
  "created_at": "2026-09-26 21:18:26",
  "updated_at": "2026-09-26 21:18:26"
}