{
  "id": 4965,
  "curve_key": "355493427229817332147791961:-14838463093939780839232498159652327086685",
  "ainvs": [
    "1",
    "1",
    "0",
    "-7406113067287861086412332",
    "17174147099464253053852169594515299360"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 184.99608258809076,
  "faltings_height": 13.4646486197305,
  "conductor": "100584989890605528503345116207040193702",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "19",
    "29",
    "31",
    "47",
    "61",
    "89",
    "179",
    "181",
    "397",
    "503",
    "601",
    "743",
    "787",
    "887"
  ],
  "discriminant": "-101420312542914153169999262352206139313659870158390604964054447885193788783248",
  "regulator": "75665324902784.82935730734509503648005401260351197888715623133095",
  "points": [
    [
      "-3169657488919",
      "2967205708271852970"
    ],
    [
      "-1257434182381",
      "4949613384940794544"
    ],
    [
      "710510444261",
      "3502956954468451710"
    ],
    [
      "10420571053340459/2809",
      "950394860711859351788313/148877"
    ],
    [
      "10397001896201",
      "32619992214022301194"
    ],
    [
      "-1902633633409",
      "4937379315458258500"
    ],
    [
      "7058524654492649/4096",
      "809211751309411613429461/262144"
    ],
    [
      "15823708986289/9",
      "83603095928414002030/27"
    ],
    [
      "25108204871059",
      "125139843067908369469"
    ],
    [
      "186471271241299/36",
      "2344217420276511373679/216"
    ],
    [
      "-3818749635810941/1089",
      "5651499035861997735040/35937"
    ],
    [
      "11891398194769759/900",
      "1273848857865808307237713/27000"
    ],
    [
      "642175411238671/729",
      "66263833021719644324756/19683"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4611, submitted by Andrii Prokhorenkov: https://elliptic-rank.icarm.cloud/curve/4611.\r\n\r\nThe source commentary identifies X660 at T = 135/64. The source model is y^2 + x*y = x^3 + x^2 - 9682089825240363517751292*x + 11586062042591897085329683155674638800.\r\n\r\nApplied a rational degree-2 isogeny and converted the target to its minimal model y^2 + x*y = x^3 + x^2 - 7406113067287861086412332*x + 17174147099464253053852169594515299360.\r\n\r\nThirteen 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 100584989890605528503345116207040193702. Source-attributed existing curve.",
  "created_at": "2026-10-21 00:00:08",
  "updated_at": "2026-10-21 00:00:08"
}