{
  "id": 4766,
  "curve_key": "-8591650499320643933614224:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "178992718735846748616963",
    "0"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 172.23849927402867,
  "faltings_height": 12.421448684477213,
  "conductor": "113914287503822021953053632003640671122813665312",
  "bad_primes": [
    "2",
    "3",
    "19",
    "43",
    "47",
    "67",
    "109",
    "127",
    "137",
    "233",
    "593",
    "29501"
  ],
  "discriminant": "-367016904416987949210085997608735791527509255137467429227321669821974208",
  "regulator": "1547116916961.9386157068588757311731399190223531028116272994743",
  "points": [
    [
      "1815169595587",
      "-2511094727517482278"
    ],
    [
      "3108488718201/25",
      "-19436677436460539574/125"
    ],
    [
      "23105147088064",
      "111080007661807727576"
    ],
    [
      "1355857371084",
      "1653852449601640314"
    ],
    [
      "1976996525091",
      "-2842708052312298198"
    ],
    [
      "52048932822297/121",
      "526693873308984736182/1331"
    ],
    [
      "250967178729/16",
      "3393473035525650549/64"
    ],
    [
      "127512964313347",
      "1439905210956249140422"
    ],
    [
      "3811061429424",
      "-7485634881031236156"
    ],
    [
      "101099605527603",
      "1016548243412394901554"
    ],
    [
      "237683398557369/196",
      "3880966074347686800069/2744"
    ],
    [
      "845515222401/16",
      "-6272780001797684673/64"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + a x with a = 178992718735846748616963 (2-isogenous model of the curve listed there). 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 21:29:13",
  "updated_at": "2026-10-20 21:29:13"
}