{
  "id": 4911,
  "curve_key": "21826542666002798249822016:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-454719638875058296871292",
    "0"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 175.03550704356408,
  "faltings_height": 12.65453266527183,
  "conductor": "45948877773036317495588418797306267208003055392",
  "bad_primes": [
    "2",
    "3",
    "7",
    "43",
    "47",
    "71",
    "73",
    "197",
    "199",
    "577",
    "2141",
    "3557"
  ],
  "discriminant": "6017430847008748947744198740812545488666640829817066345754008689134661632",
  "regulator": "6818759474832383.5833875493500868352460990527868240681392289146",
  "points": [
    [
      "104779565243721/4",
      "-1072187992296348297957/8"
    ],
    [
      "170658977449801/16",
      "2224969435774622791493/64"
    ],
    [
      "619662394934361/676",
      "-10448710088620323600387/17576"
    ],
    [
      "2835048767270976/3721",
      "-70265996542709653185648/226981"
    ],
    [
      "119368320187561/16",
      "-1298830001366617930603/64"
    ],
    [
      "430024952383849/484",
      "-5806396330003670521301/10648"
    ],
    [
      "101161318834403584/71289",
      "-28310209196139339340364704/19034163"
    ],
    [
      "913869103351824/1225",
      "11816635519231759013832/42875"
    ],
    [
      "2160656366745321/2116",
      "-75417618451541038824213/97336"
    ],
    [
      "59170448526289/36",
      "415083136995657498311/216"
    ],
    [
      "80000162606961/64",
      "-602495052206080830327/512"
    ],
    [
      "403954339983552576/570025",
      "-78943662528262152838195824/430368875"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4765, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4765.\r\n\r\nThe source commentary identifies #4765 as a 2-isogenous model of a curve listed in Aguirre, Castañeda and Peral, High rank elliptic curves with torsion group Z/(2Z), Mathematics of Computation 73 (2004), 323–331: https://doi.org/10.1090/S0025-5718-03-01547-3.\r\n\r\nApplied the standard degree-2 isogeny with kernel generated by (0,0), sending y^2 = x^3 + A*x to y^2 = x^3 - 4*A*x. Here A = 113679909718764574217823, giving y^2 = x^3 - 454719638875058296871292*x. The coordinate map is X = (x^2+A)/x, Y = y*(x^2-A)/x^2.\r\n\r\nTwelve supplied rational points transported through this map and checked exactly on the target curve. Rational torsion C2. Same rank and conductor as the source; conductor 45948877773036317495588418797306267208003055392. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:45:08",
  "updated_at": "2026-10-20 22:45:08"
}