{
  "id": 4984,
  "curve_key": "743686252892742928467025:-917395526316263472519602360937493625",
  "ainvs": [
    "1",
    "1",
    "1",
    "-15493463601932144343063",
    "1061800377674404890767253227979156"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 165.61369354894723,
  "faltings_height": 11.826140386656778,
  "conductor": "26320902315447160074455486175",
  "bad_primes": [
    "3",
    "5",
    "19",
    "29",
    "71",
    "149",
    "571",
    "1861",
    "8521",
    "9391",
    "708041"
  ],
  "discriminant": "-249018842002506028588932237404394542966764817290109391773359367109375",
  "regulator": "1181080937.3952202627924101672664919978227291737371126937",
  "points": [
    [
      "51220296369",
      "20064818985008867"
    ],
    [
      "57086568220",
      "19062231904403552"
    ],
    [
      "72047953045",
      "17875150748233577"
    ],
    [
      "-1349090887154/9",
      "108233434670013209/27"
    ],
    [
      "2611319813245/16",
      "3434867939092017953/64"
    ],
    [
      "444838386232534/4761",
      "6810925680101793860278/328509"
    ],
    [
      "2473029808864185/4489",
      "120202609338710037191921/300763"
    ],
    [
      "7945428485420990/44521",
      "592696280121796819526802/9393931"
    ],
    [
      "801615885689940970/2819041",
      "663472062201634101516379678/4733169839"
    ]
  ],
  "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. Nine rational points checked exactly; PARI/GP returned rank bounds [9,9]. Rational torsion C4. Source-attributed existing curve.",
  "created_at": "2026-10-21 01:10:03",
  "updated_at": "2026-10-21 01:10:03"
}