{
  "id": 4926,
  "curve_key": "0:-23300477422990418016",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "26968145165498169"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 89.19001104902331,
  "faltings_height": 5.490156829876905,
  "conductor": "35915103884809000742847108264324",
  "bad_primes": [
    "2",
    "3",
    "998820191314747"
  ],
  "discriminant": "-314185328784309138498426503096306352",
  "regulator": "1800389316206584.13810950663803342143097521190098316685228960",
  "points": [
    [
      "-2952350679769457/10284190921",
      "59996187505479105950696/1042930085489531"
    ],
    [
      "-100859668763297/24753043561",
      "639540280525915508039596/3894421096495691"
    ],
    [
      "1335754957762383/30516945481",
      "876821776297946290542096/5331035723021371"
    ],
    [
      "4421059874056543/41376034921",
      "1413044908770171545713196/8416340639315531"
    ],
    [
      "8486559416649075/53808689089",
      "2193799106131211898999306/12481840181908063"
    ],
    [
      "18278859892840159/79165137769",
      "4414428225347050503396260/22274140658099147"
    ],
    [
      "27848579257609359/100465543369",
      "6996022261432649645861880/31843860022868347"
    ],
    [
      "50751619624543443/144180443521",
      "14544822423222140220423054/54746900389802431"
    ],
    [
      "1466608434929539215/1293194272969",
      "1792459352454563265743454264/1470603715694798203"
    ],
    [
      "2933501156515495759/2051090858569",
      "5047448965487371737114527600/2937496437280754747"
    ],
    [
      "122154831763316657295/24619727177929",
      "1350249149361189553521683447304/122158827044081916283"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4751, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4751.\r\n\r\nThe source commentary attributes the original Mordell curve y^2 = x^3 - 998820191314747 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 = -998820191314747, giving y^2 = x^3 + 26968145165498169. The coordinate map is X = (x^3+4*B)/x^2, Y = y*(x^3-8*B)/x^3.\r\n\r\nEleven 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 35915103884809000742847108264324. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:59:15",
  "updated_at": "2026-10-20 22:59:15"
}