{
  "id": 1632,
  "curve_key": "315982448540345102566835390641:-310204226646330163876443267837238238798515561",
  "ainvs": [
    "1",
    "0",
    "0",
    "-6582967677923856303475737305",
    "359032669729548252202280621897667116372025"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    7
  ],
  "naive_height": 204.8916095639037,
  "faltings_height": 15.113873723831555,
  "conductor": "9839692872536169822270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "199",
    "541",
    "941",
    "5082541003"
  ],
  "discriminant": "-37429064694956097356266175978815006278562024211322773990674372018934784112559070000000",
  "regulator": "470999.5712833991032633899245384203168086548213",
  "points": [
    [
      "104798746251842024260/4206601",
      "3958373849776665843538030489745/8627738651"
    ],
    [
      "-696684585583435200927557630/7702118022361",
      "9897711369171457389475237029485316346415/21375449381799790109"
    ],
    [
      "196538669050538471958423243790/301859455054609",
      "86508795101790563741277234171715613274420365/5244537263642647390727"
    ],
    [
      "99047383022224548938537606290889410/407242274254935090409",
      "29796068597852254090830580087695581650323330107956055/8218248727508713417088293833077"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/7. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-25 01:57:19",
  "updated_at": "2026-09-25 01:57:19"
}