{
  "id": 3397,
  "curve_key": "15223872963729:-59400175459994202681",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-317164020078",
    "68750282369702013"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    7
  ],
  "naive_height": 91.06165770825802,
  "faltings_height": 5.025566441758555,
  "conductor": "89409298",
  "bad_primes": [
    "2",
    "11",
    "43",
    "94513"
  ],
  "discriminant": "-8202372212184655527515930624",
  "regulator": "87.5764172035893289493707370263619222385856",
  "points": [
    [
      "26338009/81",
      "-106265557/729"
    ],
    [
      "24802251841/157609",
      "9429894986994991/62570773"
    ]
  ],
  "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 = 1/44; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 89409298, torsion ℤ/7ℤ.",
  "created_at": "2026-09-26 21:20:34",
  "updated_at": "2026-09-26 21:20:34"
}