{
  "id": 4674,
  "curve_key": "12212641609:-1339714175083973",
  "ainvs": [
    "1",
    "1",
    "0",
    "-254430033",
    "1550489097537"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 69.67721234898787,
  "faltings_height": 3.6583685004587396,
  "conductor": "423625044939673170",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "43",
    "151",
    "2161",
    "5381689"
  ],
  "discriminant": "15430851508210401178664100",
  "regulator": "23384.1088294824406200534432265512570511736257300628682",
  "points": [
    [
      "-1119",
      "1354737"
    ],
    [
      "-15824",
      "1278577"
    ],
    [
      "7976",
      "165247"
    ],
    [
      "64299/4",
      "-10229619/8"
    ],
    [
      "8336",
      "90207"
    ],
    [
      "8556",
      "237"
    ],
    [
      "-904",
      "-1333623"
    ],
    [
      "14232",
      "-908439"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. I checked the eight supplied rational points exactly on this minimal model. The source records rank 8 with independent points and a matching 2-descent upper bound. Rational torsion Z/2Z. Source-attributed existing curve.",
  "created_at": "2026-10-20 20:24:36",
  "updated_at": "2026-10-20 20:24:36"
}