{
  "id": 4974,
  "curve_key": "2208377851357275283600:-103027176150309286817947337224000",
  "ainvs": [
    "0",
    "1",
    "0",
    "-46007871903276568408",
    "119244416825299791330791302688"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 147.43963558494337,
  "faltings_height": 10.13798589726507,
  "conductor": "43313662056461895042600",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "19",
    "31",
    "103",
    "227",
    "233",
    "349",
    "653",
    "5807"
  ],
  "discriminant": "89994911819971857905864488456056084801206306476206960000000",
  "regulator": "135844949.143948783079367205983441666309474295953945415",
  "points": [
    [
      "651942487",
      "299210669701092"
    ],
    [
      "2567134484",
      "134364799253124"
    ],
    [
      "11941169428",
      "1128080764011900"
    ],
    [
      "-73028134391548/9409",
      "85481545298935083300/912673"
    ],
    [
      "14549481437/4",
      "36522181637325/8"
    ],
    [
      "18529311956/49",
      "109492052512594212/343"
    ],
    [
      "100229347665428/22801",
      "151790169150811647900/3442951"
    ],
    [
      "2827180994927492/113569",
      "145239551286031507571100/38272753"
    ]
  ],
  "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 00:49:20",
  "updated_at": "2026-10-21 00:49:20"
}