{
  "id": 3366,
  "curve_key": "28666438256035321:-4841546374206426547978381",
  "ainvs": [
    "1",
    "0",
    "1",
    "-597217463667403",
    "5603641587044871717506"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    6,
    2
  ],
  "naive_height": 113.68351030395486,
  "faltings_height": 7.281282528303601,
  "conductor": "27919716630",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "19",
    "103",
    "157",
    "233"
  ],
  "discriminant": "67416222327442166556471745892540167313062500",
  "regulator": "139.59816769622436289238891703411391667532589",
  "points": [
    [
      "368900734/25",
      "251162339917/125"
    ],
    [
      "919744345/49",
      "10880844905246/343"
    ],
    [
      "1316704285/49",
      "32460742331996/343"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/2ℤ × ℤ/6ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with c=(10-2t)/(t^2-9), b=c+c^2, at t = -5/103; converted to the global minimal model. The 3 witness points were found with PARI/GP ellrank. Conductor 27919716630, torsion ℤ/2ℤ × ℤ/6ℤ.",
  "created_at": "2026-09-26 21:13:22",
  "updated_at": "2026-09-26 21:13:22"
}