{
  "id": 3398,
  "curve_key": "66145159097994769:-17011675166607103225090681",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1378024147874891",
    "19689438735404357150577"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    7
  ],
  "naive_height": 116.19188430634038,
  "faltings_height": 7.1781430259806225,
  "conductor": "61672312002",
  "bad_primes": [
    "2",
    "3",
    "7",
    "19",
    "43",
    "1797293"
  ],
  "discriminant": "12886301283878849892317524094184479932416",
  "regulator": "175.71232655300406086655367641603665116586857",
  "points": [
    [
      "20127214",
      "10347628129"
    ],
    [
      "-1062012254/25",
      "4953390239141/125"
    ],
    [
      "403028721694/18769",
      "812046681978713/2571353"
    ]
  ],
  "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 = 133/4; converted to the global minimal model. The 3 witness points were found with PARI/GP ellrank. Conductor 61672312002, torsion ℤ/7ℤ.",
  "created_at": "2026-09-26 21:20:43",
  "updated_at": "2026-09-26 21:20:43"
}