{
  "id": 4966,
  "curve_key": "1583747252466971849789948721:52645581896156142398213704459080033525975",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-32994734426395246870623932",
    "-60932386453876175388400003571476827265"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 187.88877368599037,
  "faltings_height": 13.656327307138431,
  "conductor": "27184304298374298547706309213830981063446",
  "bad_primes": [
    "2",
    "3",
    "7",
    "17",
    "41",
    "43",
    "67",
    "103",
    "167",
    "173",
    "271",
    "379",
    "563",
    "1009",
    "1663",
    "2441",
    "2731",
    "55819"
  ],
  "discriminant": "694956736817299408067429326383068460972919112829012431387530210104430057408512",
  "regulator": "14649220022338242.4198744795690636309866475645852846320972219875320",
  "points": [
    [
      "-2317778439227",
      "1758058966472598229"
    ],
    [
      "-2273680372487",
      "1527425288935926729"
    ],
    [
      "-2241920235435",
      "-1330721469867587771"
    ],
    [
      "-2756557218435",
      "-3012222052705715795"
    ],
    [
      "-3740230525065",
      "-3186254293577319035"
    ],
    [
      "-4353384568875",
      "-448576922213514011"
    ],
    [
      "9364545695793",
      "-21244017753742387871"
    ],
    [
      "1564125061193395/169",
      "-45371036011019714851757/2197"
    ],
    [
      "8361099982173",
      "-15738589199893910771"
    ],
    [
      "174222113044646487/24649",
      "29717233130802590001828151/3869893"
    ],
    [
      "-308870127626495483/142129",
      "38174588944302898500270957/53582633"
    ],
    [
      "174796118487685/9",
      "-2197519322114675843017/27"
    ],
    [
      "-87906325660431/25",
      "-425924722738029283063/125"
    ],
    [
      "-15049904391565151/4225",
      "-927248851929208965005487/274625"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4612, submitted by Andrii Prokhorenkov: https://elliptic-rank.icarm.cloud/curve/4612.\r\n\r\nThe source commentary identifies X660 at T = 75/41. The source model is y^2 + x*y + y = x^3 - x^2 - 9587363242690973783330492*x + 10536060714562308983254191000903086975.\r\n\r\nApplied a rational degree-2 isogeny and converted the target to its minimal model y^2 + x*y + y = x^3 - x^2 - 32994734426395246870623932*x - 60932386453876175388400003571476827265.\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 27184304298374298547706309213830981063446. Source-attributed existing curve.",
  "created_at": "2026-10-21 00:02:20",
  "updated_at": "2026-10-21 00:02:20"
}