{
  "id": 4758,
  "curve_key": "75698258016:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1577047042",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 75.1500629563421,
  "faltings_height": 4.330745658003332,
  "conductor": "159172951851580784896",
  "bad_primes": [
    "2",
    "41",
    "2593",
    "7417"
  ],
  "discriminant": "251023232883943899844275077632",
  "regulator": "1001049.564428045052089109962758498520935217667868105",
  "points": [
    [
      "-7417",
      "3359901"
    ],
    [
      "-23337",
      "4908549"
    ],
    [
      "-304097/81",
      "1765891279/729"
    ],
    [
      "1498754/25",
      "1374533742/125"
    ],
    [
      "-289",
      "675087"
    ],
    [
      "-21689/81",
      "473715107/729"
    ],
    [
      "1201554/25",
      "741892842/125"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + a x with a = -1577047042. Source: Aguirre, Lozano-Robledo, Peral, 'Elliptic curves of maximal rank', Table 2 (Rev. Mat. Iberoamericana proc. 2008; preprint https://alozano.clas.uconn.edu/wp-content/uploads/sites/490/2014/01/ALP-2-23-07.pdf).",
  "created_at": "2026-10-20 21:28:45",
  "updated_at": "2026-10-20 21:28:45"
}