{
  "id": 4918,
  "curve_key": "-18033191586955036171978303921344:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "375691491394896586916214665028",
    "0"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 215.90930048019604,
  "faltings_height": 16.060682118324493,
  "conductor": "31365354823671479158815749670876719302406866939637832497952",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "29",
    "31",
    "43",
    "47",
    "59",
    "79",
    "83",
    "173",
    "313",
    "373",
    "1487",
    "3457"
  ],
  "discriminant": "-3393704716368552479990825843551330631783388798661900488380557118471138205010290482694524928",
  "regulator": "1256929426486255360.537298287201529229121430741895798343250649853",
  "points": [
    [
      "63016352864656",
      "-4891313663433900760472"
    ],
    [
      "16405596103886224",
      "-2102765885235988356634264"
    ],
    [
      "91094570804206637056/442225",
      "-2729242154387650557652657767296/294079625"
    ],
    [
      "713400755650969/196",
      "-3208826168567475874703011/2744"
    ],
    [
      "54766595564524321/196",
      "30898029785886176769990737/2744"
    ],
    [
      "8167519884446224/9",
      "890723253669188662757384/27"
    ],
    [
      "27637297950664249/16",
      "-4875243635568196832873491/64"
    ],
    [
      "159943032271718656/729",
      "189803873200090995956836448/19683"
    ],
    [
      "2001968622036496/9",
      "262574895009664781267192/27"
    ],
    [
      "27188222681034686209/27556",
      "166894096665028594493841213601/4574296"
    ],
    [
      "69688329427062784/9",
      "18454254189831162575346304/27"
    ],
    [
      "196316738772296704/488601",
      "-132693237385765051998757472576/341532099"
    ],
    [
      "13490311365409161031620496/31562720281",
      "-86625888245138825327413929876094697048/5607401322402179"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4774, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4774.\r\n\r\nThe source commentary attributes the original curve y^2 = x^3 - 93922872848724146729053666257*x to 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 = -93922872848724146729053666257, giving y^2 = x^3 + 375691491394896586916214665028*x. The coordinate map is X = (x^2+A)/x, Y = y*(x^2-A)/x^2.\r\n\r\nThirteen 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 31365354823671479158815749670876719302406866939637832497952. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:52:31",
  "updated_at": "2026-10-20 22:52:31"
}