{
  "id": 4929,
  "curve_key": "0:-133470441634383072",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "154479677817573"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 78.86531287451511,
  "faltings_height": 4.629765315334555,
  "conductor": "3535403090166097125372979308",
  "bad_primes": [
    "2",
    "3",
    "13063",
    "437990473"
  ],
  "discriminant": "-10309235410924339217587607662128",
  "regulator": "19039548576986.79466820552133418955847494968527548941162401",
  "points": [
    [
      "-17136108659321/320947225",
      "8667260220472192342/5749769535875"
    ],
    [
      "-15954061021433/363550489",
      "57982258085193636490/6931817173763"
    ],
    [
      "-3931459073093/92871769",
      "7935832941484342060/895005237853"
    ],
    [
      "-3109966834799/119464900",
      "15274374388065612199/1305751357000"
    ],
    [
      "-273356523407/195049156",
      "33856956943463030185/2724056512696"
    ],
    [
      "4175796051043/290395681",
      "62095588917280378640/4948632799921"
    ],
    [
      "16718263880407/501177769",
      "155304533087177497390/11219866714603"
    ],
    [
      "35487783847951/751582225",
      "332080036997573800574/20604626698375"
    ],
    [
      "99426980241457/1403401444",
      "1187390897147099365705/52574224895128"
    ],
    [
      "7666230408914179/38956890625",
      "678001425815659032390592/7689116287109375"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4750, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4750.\r\n\r\nThe source commentary attributes the original Mordell curve y^2 = x^3 - 5721469548799 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 = -5721469548799, giving y^2 = x^3 + 154479677817573. 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 3535403090166097125372979308. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:02:57",
  "updated_at": "2026-10-20 23:02:57"
}