{
  "id": 1687,
  "curve_key": "1340767182025:-2764107107579205125",
  "ainvs": [
    "1",
    "1",
    "0",
    "-27932649625",
    "3199186402575625"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    4
  ],
  "naive_height": 84.92649865996118,
  "faltings_height": 5.117741642705313,
  "conductor": "9680213412150",
  "bad_primes": [
    "2",
    "3",
    "5",
    "41",
    "61",
    "101",
    "449",
    "569"
  ],
  "discriminant": "-3026648772882909341988797590312500",
  "regulator": "10086.022056395613373688268633127829018604760097631",
  "points": [
    [
      "1388655",
      "1624803535"
    ],
    [
      "11161921/121",
      "49872754106/1331"
    ],
    [
      "26145211/49",
      "128341728493/343"
    ],
    [
      "121569600/289",
      "-1262106718675/4913"
    ],
    [
      "403100",
      "239463425"
    ],
    [
      "773650/9",
      "1021019575/27"
    ]
  ],
  "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 06:10:08",
  "updated_at": "2026-09-25 06:10:08"
}