{
  "id": 4958,
  "curve_key": "77299156682436614595246802036316736:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1610399097550762804067641709089932",
    "0"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 240.9989733439993,
  "faltings_height": 18.1514881903081,
  "conductor": "576307834087180278659283541515639524426406638619391775412369725472",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "19",
    "23",
    "37",
    "59",
    "71",
    "73",
    "97",
    "127",
    "139",
    "151",
    "263",
    "313",
    "443",
    "733"
  ],
  "discriminant": "267288657386523799316291488371228511865684311410585134071470276961952169731546386350289577990154596352",
  "regulator": "31407647857509677593.7044358471769725985943944749831213452896651420",
  "points": [
    [
      "40441384554988356",
      "-1007641356146122518370332"
    ],
    [
      "155913997889805156",
      "-59489972745861823733223468"
    ],
    [
      "159269758314511716",
      "-61511666661661829693987628"
    ],
    [
      "1709507491057673316",
      "-2234533244040834483530297772"
    ],
    [
      "313238553648232969/4",
      "150543806552511181977218309/8"
    ],
    [
      "3365051914330975089/16",
      "6059466318435097988073416841/64"
    ],
    [
      "11128315503538044036",
      "-37122850915733058332339462652"
    ],
    [
      "12958008542108666404/121",
      "43246468084923859896358748396/1331"
    ],
    [
      "28026307493591306769/16",
      "148331989779320844157452251769/64"
    ],
    [
      "8178706920738762769/100",
      "20380728188091435846632752103/1000"
    ],
    [
      "297941845134761856081/1600",
      "-5021931934655461891656626914521/64000"
    ],
    [
      "1022034756365560579041/6724",
      "-31514402561941476813878572570353/551368"
    ],
    [
      "1331388447261439608001/9216",
      "-46668053263829969319525088699103/884736"
    ],
    [
      "905792974706806258644324/21464689",
      "266649825862753600453542119439846036/99445904137"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4695, submitted by dujella: https://elliptic-rank.icarm.cloud/curve/4695.\r\n\r\nThe source commentary credits Watkins (2002). The source model is y^2 = x^3 + 402599774387690701016910427272483*x.\r\n\r\nApplied the degree-2 isogeny X = (x^2 + A)/x, Y = y*(x^2 - A)/x^2 with A = 402599774387690701016910427272483. The resulting model is Y^2 = X^3 - 1610399097550762804067641709089932*X.\r\n\r\nFourteen supplied rational points transported through this map and checked exactly on the target curve. Rational torsion Z/2Z. Same rank and conductor as the source; conductor 576307834087180278659283541515639524426406638619391775412369725472. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:50:15",
  "updated_at": "2026-10-20 23:50:15"
}