{
  "id": 3376,
  "curve_key": "80874429687745:-727270826352517317025",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1684883951828",
    "841748501204713872"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    10
  ],
  "naive_height": 96.07175645085103,
  "faltings_height": 5.678917782079936,
  "conductor": "404284650",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "29",
    "71"
  ],
  "discriminant": "29151794524080184451026155017856000",
  "regulator": "102.185202789146415934879054482652377369825",
  "points": [
    [
      "753718",
      "872200"
    ],
    [
      "30195041632756/40896025",
      "3909575829194178836/261530079875"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/10ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with d=t^2/(t-(t-1)^2), c=td-t, b=cd, at t = 14/11; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 404284650, torsion ℤ/10ℤ.",
  "created_at": "2026-09-26 21:17:02",
  "updated_at": "2026-09-26 21:17:02"
}