{
  "id": 4987,
  "curve_key": "85896451179385522348277025:-796090387459674338187164571286686812625",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1789509399570531715589105",
    "921400911412107490992444220066266272"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 179.1455542397972,
  "faltings_height": 12.498737253931628,
  "conductor": "100280923985211056168634033075",
  "bad_primes": [
    "3",
    "5",
    "7",
    "67",
    "73",
    "101",
    "127",
    "443",
    "563",
    "877",
    "929",
    "1181",
    "4229"
  ],
  "discriminant": "763322136963854740988958884865201852085383414001293692767515282890625",
  "regulator": "196173059.90198207240266823791527421505612508160808400183",
  "points": [
    [
      "534485279914",
      "342962269911201555"
    ],
    [
      "33801388468284",
      "196366131961917065620"
    ],
    [
      "-17091787174298754/12769",
      "1382843997014552600465315/1442897"
    ],
    [
      "-18339647946531/16",
      "77506866045370590955/64"
    ],
    [
      "5025892299481/9",
      "8375483969319221365/27"
    ],
    [
      "6855350848456/9",
      "435083129199805765/27"
    ],
    [
      "564835674408549/16",
      "13414536318678542214895/64"
    ],
    [
      "13025367864597156/16129",
      "110685985292577884217940/2048383"
    ],
    [
      "59402163255216486/76729",
      "55968988601041819858135/21253933"
    ]
  ],
  "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. Nine rational points checked exactly; PARI/GP returned rank bounds [9,9]. Rational torsion C4. Source-attributed existing curve.",
  "created_at": "2026-10-21 01:12:39",
  "updated_at": "2026-10-21 01:12:39"
}