{
  "id": 4975,
  "curve_key": "141363513239454621793:-1633223206216883378212960126481",
  "ainvs": [
    "1",
    "1",
    "1",
    "-2945073192488637954",
    "1890304635597982672357697295"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 139.19359906419746,
  "faltings_height": 9.511665520793342,
  "conductor": "62497082243308795337562",
  "bad_primes": [
    "2",
    "3",
    "29",
    "37",
    "61",
    "71",
    "73",
    "89",
    "149",
    "877",
    "1193",
    "2213"
  ],
  "discriminant": "91168936842587529759075406003445642750890433852469215232",
  "regulator": "91443283.0365208502864437321800582167283467164029757787",
  "points": [
    [
      "823465257",
      "4850039878851"
    ],
    [
      "1181335929",
      "7732624988163"
    ],
    [
      "20777418301/16",
      "1023394739153153/64"
    ],
    [
      "19727093781/25",
      "949627685674039/125"
    ],
    [
      "29443805815/49",
      "6302094152742065/343"
    ],
    [
      "10969721335345/1369",
      "35557373550209234807/50653"
    ],
    [
      "469752603598489/410881",
      "1105760314679097161347/263374721"
    ],
    [
      "5709615809046625/32041",
      "431409542366921499194881/5735339"
    ]
  ],
  "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 00:50:39",
  "updated_at": "2026-10-21 00:50:39"
}