{
  "id": 4973,
  "curve_key": "3847068416804226448:-7545615500942397340330901696",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-80147258683421384",
    "8733351300954638705041968"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 128.38152924588408,
  "faltings_height": 8.24818237241461,
  "conductor": "16595433408864784656",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "23",
    "29",
    "31",
    "107",
    "127",
    "131",
    "233",
    "443"
  ],
  "discriminant": "29382965618963591022620769572745503913071726592",
  "regulator": "69430.17658945720600136394469310958328254451327023255",
  "points": [
    [
      "-86895172",
      "3878354752272"
    ],
    [
      "110288066",
      "1111552669542"
    ],
    [
      "130612716",
      "702361369008"
    ],
    [
      "166292924",
      "63114762480"
    ],
    [
      "187764733",
      "551615819638"
    ],
    [
      "1483294228/9",
      "813059761384/27"
    ],
    [
      "3933420764/25",
      "16812245228688/125"
    ]
  ],
  "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. Seven rational points checked exactly; PARI/GP returned rank bounds [7,7]. Rational torsion C4. Source-attributed existing curve.",
  "created_at": "2026-10-21 00:48:01",
  "updated_at": "2026-10-21 00:48:01"
}