{
  "id": 4760,
  "curve_key": "34918329646176:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-727465200962",
    "0"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 93.55209903608001,
  "faltings_height": 5.864248664648158,
  "conductor": "33869159591083714926428416",
  "bad_primes": [
    "2",
    "41",
    "1601",
    "2137",
    "2593"
  ],
  "discriminant": "24638634988341764422319766690347336192",
  "regulator": "69256283.355129289365383471228879942511111174000552893354",
  "points": [
    [
      "3421337/4",
      "475565843/8"
    ],
    [
      "1577106",
      "-1665949638"
    ],
    [
      "5316921/4",
      "-9403270173/8"
    ],
    [
      "-627592",
      "-457559396"
    ],
    [
      "-30792033/49",
      "-156803296047/343"
    ],
    [
      "2334258",
      "-3319747146"
    ],
    [
      "14373778/9",
      "-46073107306/27"
    ],
    [
      "-706041",
      "-402073539"
    ],
    [
      "-2053657/529",
      "-646578470899/12167"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + a x with a = -727465200962. 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 21:28:53",
  "updated_at": "2026-10-20 21:28:53"
}