{
  "id": 4980,
  "curve_key": "210094371822957656193:-60125339428461564572410678879425",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-4376966079644951171",
    "69589513228480311626868042051"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 146.34796832722236,
  "faltings_height": 10.253484782340706,
  "conductor": "679633104414005058194982",
  "bad_primes": [
    "2",
    "3",
    "13",
    "19",
    "31",
    "43",
    "73",
    "241",
    "307",
    "691",
    "2131",
    "14419"
  ],
  "discriminant": "-2086679948138825945055188048836446254209751722498084495342656",
  "regulator": "24027405.6842961100880236279274622775481832595417989294",
  "points": [
    [
      "-1063441025663781/330625",
      "42676231069778921660022/190109375"
    ],
    [
      "-6090891407065/1369",
      "1595843281111838166/50653"
    ],
    [
      "-2862470086285/841",
      "5176973159261659458/24389"
    ],
    [
      "22540700661/16",
      "16469146378606535/64"
    ],
    [
      "667043788509/25",
      "544114109158854492/125"
    ],
    [
      "3453357785952071/60025",
      "202839981769368805706634/14706125"
    ],
    [
      "5933543195185871/942841",
      "494103017644549146675858/915498611"
    ],
    [
      "16156077616662569/289",
      "2053543311557265416833944/4913"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Michael Rubinstein's elliptic-curves-by-rank repository, families/family_Z4.part2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Eight rational points checked exactly; PARI/GP returned rank bounds [8,8]. Rational torsion C4. Source-attributed existing curve.",
  "created_at": "2026-10-21 01:05:09",
  "updated_at": "2026-10-21 01:05:09"
}