{
  "id": 4764,
  "curve_key": "497115987275005640256:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-10356583068229284172",
    "0"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 142.96606514268177,
  "faltings_height": 9.98207917353164,
  "conductor": "156696585608668361973767378558845472",
  "bad_primes": [
    "2",
    "11",
    "13",
    "23",
    "29",
    "31",
    "37",
    "43",
    "53",
    "59",
    "67",
    "71"
  ],
  "discriminant": "71093427524589409801900282724050219961671343907834538012672",
  "regulator": "938940960.60455470219321491488405399593028412983239966495",
  "points": [
    [
      "-324610088356879/1196836",
      "69147424517775678411753/1309338584"
    ],
    [
      "-6369046695882/2209",
      "7969476318404041116/103823"
    ],
    [
      "-707671855098/289",
      "507670107191439972/4913"
    ],
    [
      "-535100097674/1089",
      "2533560906661190108/35937"
    ],
    [
      "152382607894/9",
      "58400024944943924/27"
    ],
    [
      "215696318436/49",
      "68349921284772492/343"
    ],
    [
      "709623495097/16",
      "596205081499141587/64"
    ],
    [
      "958432317337/144",
      "821329086991786307/1728"
    ],
    [
      "1467313461238/441",
      "451372032319111084/9261"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + a x with a = -10356583068229284172. 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 21:29:06",
  "updated_at": "2026-10-20 21:29:06"
}