{
  "id": 4972,
  "curve_key": "1355376986461859728:-1577923778759186344209972416",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-28237020551288744",
    "1826300679272509563635568"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 125.25183392495957,
  "faltings_height": 8.064652973340294,
  "conductor": "15418498435441900656",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "31",
    "59",
    "67",
    "79",
    "197",
    "257",
    "4583"
  ],
  "discriminant": "27471584899559170751417857654648065052271788032",
  "regulator": "136556.3628543674037801108373458491972862332880669753",
  "points": [
    [
      "-185162284",
      "840493743648"
    ],
    [
      "70440466",
      "432189155398"
    ],
    [
      "154504964",
      "1073242714320"
    ],
    [
      "2448815426",
      "120902783834118"
    ],
    [
      "-129092203/4",
      "13155030030051/8"
    ],
    [
      "1617132164/49",
      "330839218407984/343"
    ],
    [
      "182188416698/1849",
      "2035170994116546/79507"
    ]
  ],
  "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 00:46:48",
  "updated_at": "2026-10-21 00:46:48"
}