{
  "id": 4928,
  "curve_key": "0:84262552694967168",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-97526102656212"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 77.94542789291363,
  "faltings_height": 4.553108233534431,
  "conductor": "352271877752222271180081072",
  "bad_primes": [
    "2",
    "3",
    "903019469039"
  ],
  "discriminant": "-4108899182101920571044465623808",
  "regulator": "11652030967103.03507366194299525158139355424346992763334255",
  "points": [
    [
      "11583208361197/201725209",
      "27450929394055490975/2865103143427"
    ],
    [
      "11823095069749/190302025",
      "31314079000346785307/2625216434875"
    ],
    [
      "3264782437078/31125241",
      "5644282148194311910/173647719539"
    ],
    [
      "14311322405749/26574025",
      "54123269313866463557/136989098875"
    ],
    [
      "14433731072317/5968249",
      "54836081946021459385/14580432307"
    ],
    [
      "3639760450558/5764801",
      "-6942646372451936390/13841287201"
    ],
    [
      "14983105642237/65885689",
      "-57755659610422182745/534794137613"
    ],
    [
      "3794449403158/20259001",
      "-7336278683396689510/91185763501"
    ],
    [
      "373040277920749/5047392025",
      "6274649349607581318943/358591966416125"
    ],
    [
      "205493749989118/2167926721",
      "2771971502697229801850/100940836056481"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4749, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4749.\r\n\r\nThe source commentary attributes the original Mordell curve y^2 = x^3 + 3612077876156 to Noam D. Elkies, “j=0, rank 15; also 3-rank 6 and 7 in real and imaginary quadratic fields”, NMBRTHRY post, 30 December 2009: https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;6a3fad67.0912&S=.\r\n\r\nApplied the standard degree-3 isogeny from y^2 = x^3 + B to y^2 = x^3 - 27*B. Here B = 3612077876156, giving y^2 = x^3 - 97526102656212. The coordinate map is X = (x^3+4*B)/x^2, Y = y*(x^3-8*B)/x^3.\r\n\r\nTen supplied rational points transported through this map and checked exactly on the target curve. Rational torsion trivial. Same rank and conductor as the source; conductor 352271877752222271180081072. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:01:43",
  "updated_at": "2026-10-20 23:01:43"
}