{
  "id": 4763,
  "curve_key": "49606936139605296:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1033477836241777",
    "0"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 115.32872118116686,
  "faltings_height": 7.678967176738729,
  "conductor": "34178446016095527602163203767328",
  "bad_primes": [
    "2",
    "73",
    "673",
    "2129",
    "2393",
    "4129"
  ],
  "discriminant": "70645332869641578355990850250706803718922523712",
  "regulator": "3788061946.309255772494655922282703222398654213079489567999",
  "points": [
    [
      "-25767824",
      "97576307532"
    ],
    [
      "77037849",
      "614483231376"
    ],
    [
      "-1001189475652/32041",
      "242248306123495746/5735339"
    ],
    [
      "-1722965636/81",
      "-81043257689506/729"
    ],
    [
      "-41069874752/1681",
      "-7117927801690344/68921"
    ],
    [
      "-2883562839121/273529",
      "-14106335317318398144/143055667"
    ],
    [
      "18223731169/400",
      "-1743206625311697/8000"
    ],
    [
      "14157230633449/329476",
      "35344219980706467501/189119224"
    ],
    [
      "-26598836324/2209",
      "10738734889670358/103823"
    ],
    [
      "-25009353/49",
      "-7876679054448/343"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + a x with a = -1033477836241777. 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 21:29:02",
  "updated_at": "2026-10-20 21:29:02"
}