{
  "id": 4769,
  "curve_key": "78963711578321325432217200:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1645077324548360946504525",
    "0"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 178.89309189504618,
  "faltings_height": 12.975998069562005,
  "conductor": "3464037636791287415327029772074929316884282208800",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "31",
    "43",
    "47",
    "61",
    "67",
    "73",
    "197",
    "251",
    "271",
    "419"
  ],
  "discriminant": "284930488383371900247961754132105193825609265627970786467479000309741000000",
  "regulator": "453739398352.91129366342155065430200215001782034416117053915068",
  "points": [
    [
      "6452826676905",
      "16064671526784139350"
    ],
    [
      "-152160578405",
      "496782615891022450"
    ],
    [
      "-18280131891975/16",
      "39874092186704525325/64"
    ],
    [
      "-1258605889845",
      "277056914531579850"
    ],
    [
      "1315287167920",
      "-334173366644474500"
    ],
    [
      "1465715472780",
      "-858844155457885350"
    ],
    [
      "58768107612505",
      "450411118044836946050"
    ],
    [
      "1365200765625",
      "546409811106791250"
    ],
    [
      "-1101502139991",
      "689634668272172502"
    ],
    [
      "-3413830263855/4",
      "7076061679895292975/8"
    ],
    [
      "5741529645105/4",
      "-6176268700616275425/8"
    ],
    [
      "2531821884780",
      "3473362136846698350"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + a x with a = -1645077324548360946504525. Source: Aguirre, Castaneda, Peral, 'High rank elliptic curves with torsion group Z/(2Z)', Math. Comp. 73 (2004) 323-331, doi:10.1090/S0025-5718-03-01547-3, https://www.ams.org/mcom/2004-73-245/S0025-5718-03-01547-3/.",
  "created_at": "2026-10-20 21:29:26",
  "updated_at": "2026-10-20 21:29:26"
}