{
  "id": 1690,
  "curve_key": "19484342877025:-70496270896066168625",
  "ainvs": [
    "1",
    "1",
    "1",
    "-405923809938",
    "81592736994785406"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    4
  ],
  "naive_height": 91.8018969887834,
  "faltings_height": 5.653625136232413,
  "conductor": "33309463270425",
  "bad_primes": [
    "3",
    "5",
    "31",
    "41",
    "59",
    "61",
    "79",
    "1229"
  ],
  "discriminant": "1404689967527888345795098904382890625",
  "regulator": "2041.3272286000935485272246762640743493279308847987",
  "points": [
    [
      "678015",
      "-343933708"
    ],
    [
      "4458856/9",
      "1227488926/27"
    ],
    [
      "140815",
      "164928992"
    ],
    [
      "578890",
      "-201788458"
    ],
    [
      "182293315/196",
      "-1958174000777/2744"
    ],
    [
      "490390",
      "-21744058"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/4. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-25 06:10:38",
  "updated_at": "2026-09-25 06:10:38"
}