{
  "id": 3505,
  "curve_key": "3257516313:21272431252995",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-67864923",
    "-24603903275"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2,
    2
  ],
  "naive_height": 65.71269262433647,
  "faltings_height": 3.543498075239581,
  "conductor": "5037649974",
  "bad_primes": [
    "2",
    "3",
    "7",
    "37",
    "47",
    "83",
    "277"
  ],
  "discriminant": "19742090906990030918676624",
  "regulator": "118.180183461319809084125619453703171974555209967",
  "points": [
    [
      "154826",
      "60756773"
    ],
    [
      "-38374/25",
      "34544209/125"
    ],
    [
      "-2233",
      "341411"
    ],
    [
      "15218",
      "1562981"
    ],
    [
      "-7854",
      "-150619"
    ]
  ],
  "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": "2026-09-27 12:21:05",
  "updated_at": "2026-09-27 12:21:05"
}