{
  "id": 1340,
  "curve_key": "168367265730441:-2184343160575545901989",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-3507651369384",
    "2528175831282687140"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    3
  ],
  "naive_height": 98.27150644445473,
  "faltings_height": 5.898018121803712,
  "conductor": "33742365235013610",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "23",
    "37",
    "4783",
    "5059"
  ],
  "discriminant": "834555502253538549546430296304687500",
  "regulator": "3947.671028097308241175251168435050697337318324926419",
  "points": [
    [
      "1617376",
      "1041249322"
    ],
    [
      "-1156514",
      "-2243961068"
    ],
    [
      "-1924064",
      "1468678282"
    ],
    [
      "5007686",
      "-10516317468"
    ],
    [
      "970135",
      "195305335"
    ],
    [
      "10053424/9",
      "1651068614/27"
    ],
    [
      "11788306",
      "39985740292"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/3. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-24 17:35:02",
  "updated_at": "2026-09-24 17:35:02"
}