{
  "id": 4978,
  "curve_key": "7447769618444396820913:-642745890969661109579008688750825",
  "ainvs": [
    "1",
    "1",
    "1",
    "-155161867050924933769",
    "743918855224308839630411704391"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 151.08660468110608,
  "faltings_height": 10.105933764836747,
  "conductor": "150499654534627570835598",
  "bad_primes": [
    "2",
    "3",
    "13",
    "17",
    "41",
    "103",
    "127",
    "2089",
    "2729",
    "4241",
    "8753"
  ],
  "discriminant": "46618057728344267661960641101190073923037520822456003824",
  "regulator": "461994930.914657611760846612870068006535732979250685626",
  "points": [
    [
      "-13968391747",
      "431080436805816"
    ],
    [
      "6622480457",
      "82496306269350"
    ],
    [
      "233862242225149/11449",
      "3024932034908652381752/1225043"
    ],
    [
      "2327218025301473/323761",
      "84137085424115307774/184220009"
    ],
    [
      "140841302184062747/19589476",
      "11756090883771435556785/86703020776"
    ],
    [
      "82188563993207297/11771761",
      "1238762606635114858116672/40388911991"
    ],
    [
      "1517096259587714761/166900561",
      "627030888437518289700465946/2156188347559"
    ],
    [
      "5698953053954925085/463153441",
      "8325611899734880032026658602/9967525203761"
    ]
  ],
  "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 00:54:42",
  "updated_at": "2026-10-21 00:54:42"
}