{
  "id": 4981,
  "curve_key": "-824141851744143462047:-7835001429215641566507720000049",
  "ainvs": [
    "1",
    "0",
    "0",
    "17169621911336322126",
    "9068288692652609194587887955"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 144.48262301748326,
  "faltings_height": 10.116601790724987,
  "conductor": "1349320766930761037785491",
  "bad_primes": [
    "3",
    "7",
    "19",
    "37",
    "67",
    "139",
    "193",
    "2293",
    "3943",
    "803461"
  ],
  "discriminant": "-359463230862002161703834184663950532004149748016654531763183",
  "regulator": "36830136.1680030125765808777743966558735070920783686763",
  "points": [
    [
      "-411140187",
      "44041885062705"
    ],
    [
      "347335293",
      "122775261607122"
    ],
    [
      "725515587",
      "148009801528053"
    ],
    [
      "12110692458",
      "1411824635281275"
    ],
    [
      "-1426352190923169/3996001",
      "429738436913302909651572/7988005999"
    ],
    [
      "664352883063/676",
      "2882202659817175557/17576"
    ],
    [
      "1216602507579/169",
      "1562390911791847272/2197"
    ],
    [
      "4581617274039/625",
      "11362866338850863037/15625"
    ]
  ],
  "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 01:06:24",
  "updated_at": "2026-10-21 01:06:24"
}