{
  "id": 4773,
  "curve_key": "-1396036421958913527626838308304:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "29084092124144031825559131423",
    "0"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 208.23356965214896,
  "faltings_height": 15.421037882653904,
  "conductor": "1323698042444241813123724539916763571371277542214384672",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "19",
    "31",
    "37",
    "59",
    "79",
    "223",
    "599",
    "919",
    "1871",
    "2903"
  ],
  "discriminant": "-1574513935558173533083864989903024250534304858231944822112438363712683994078696754173888",
  "regulator": "7368740603302.4545537957003327274177702390166138522137825731464",
  "points": [
    [
      "12310556095473727/81",
      "-2052990864449262770385808/729"
    ],
    [
      "239067343399872",
      "4540541714194976405448"
    ],
    [
      "20684427680631",
      "781305023985244296252"
    ],
    [
      "489388396494612433/19321",
      "-2330355868192118945932510484/2685619"
    ],
    [
      "7786014892179601/36",
      "-874918363083623177631697/216"
    ],
    [
      "81933434051953",
      "-1712596235382928568464"
    ],
    [
      "442489649227498873/149769",
      "-16992857133628121629124585344/57960603"
    ],
    [
      "113147149220625",
      "-2176998690911041537800"
    ],
    [
      "3139601972092663",
      "176177991751057927251236"
    ],
    [
      "1410294126554751/529",
      "-3388373954648688170532912/12167"
    ],
    [
      "268540855122324648721/1585081",
      "6244098006399203778653546738732/1995616979"
    ],
    [
      "15264229403426803228/76729",
      "-78550476509928003934462429034/21253933"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + a x with a = 29084092124144031825559131423 (2-isogenous model of the curve listed there). Source: Aguirre, Castaneda, Peral, 'High rank elliptic curves with torsion group Z/(2Z)', Math. Comp. 73 (2004) 323-331, doi:10.1090/S0025-5718-03-01547-3, https://www.ams.org/mcom/2004-73-245/S0025-5718-03-01547-3/.",
  "created_at": "2026-10-20 21:29:50",
  "updated_at": "2026-10-20 21:29:50"
}