{
  "id": 4103,
  "curve_key": "12764724422800:-2768686251480440000",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-265931758808",
    "3204586620170112"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2,
    2
  ],
  "naive_height": 90.53311973366746,
  "faltings_height": 5.612442792005862,
  "conductor": "109507405690597200",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "29",
    "31",
    "47",
    "73",
    "313",
    "661"
  ],
  "discriminant": "1199187190108504002145649264784000000",
  "regulator": "8613.278476488322405837470029741672598748836131513074",
  "points": [
    [
      "-199208",
      "219715600"
    ],
    [
      "-388618",
      "-218768550"
    ],
    [
      "566492",
      "185339700"
    ],
    [
      "-40868",
      "118340300"
    ],
    [
      "-25684",
      "100089132"
    ],
    [
      "-432948",
      "-192835500"
    ],
    [
      "-519748",
      "-31908300"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/2+Z/2. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-10-09 14:52:22",
  "updated_at": "2026-10-09 14:52:22"
}