{
  "id": 1618,
  "curve_key": "133821321783282120482784961:-1221852470583033382675270077237140267041",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2787944203818377510058020",
    "1414181100211611864227540687565296400"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    6,
    2
  ],
  "naive_height": 180.47564316745613,
  "faltings_height": 13.050858886086814,
  "conductor": "3845501537362524390",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "23",
    "29",
    "31",
    "73",
    "661",
    "2459",
    "4019"
  ],
  "discriminant": "522898339387370986301562653628353200877869247782082620839127000878144000000",
  "regulator": "15606.13015871309311576292879646409757738723748",
  "points": [
    [
      "55817343460087019140/102596641",
      "251220678791542174322074115020/1039201376689"
    ],
    [
      "-61375901179027160/52441",
      "21055025668546338264613420/12008989"
    ],
    [
      "106152431881266772360/200873929",
      "846759912370808066339751072460/2846986195717"
    ],
    [
      "5086679025623293600/3690241",
      "3092114781710484847366157380/7088952961"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/6+Z/2. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-25 01:41:11",
  "updated_at": "2026-09-25 01:41:11"
}