{
  "id": 4882,
  "curve_key": "-18870192:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "393129",
    "0"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 50.2592822765212,
  "faltings_height": 2.2565139346849237,
  "conductor": "25160256",
  "bad_primes": [
    "2",
    "3",
    "11",
    "19"
  ],
  "discriminant": "-3888527896632684096",
  "regulator": "181.50451538917888451956276892179582939838190",
  "points": [
    [
      "3249/16",
      "601065/64"
    ],
    [
      "4356/25",
      "1073754/125"
    ],
    [
      "9801/16",
      "1388475/64"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4719, submitted by David Renshaw and sourced to Table 2 of Watkins, Donnelly, Elkies, Fisher, Granville and Rogers, Ranks of quadratic twists of elliptic curves (2014): https://doi.org/10.5802/pmb.9. Three rational points transported through the isogeny and checked exactly. Rational torsion C2. Same rank and conductor as the source. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:25:52",
  "updated_at": "2026-10-20 22:25:52"
}