{
  "id": 4776,
  "curve_key": "928704304074574819996808333083200:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-19348006334886975416600173605900",
    "0"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 227.7340295493244,
  "faltings_height": 17.046076207418523,
  "conductor": "29947627930786122521100129658764695285207276277281520681184800",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "23",
    "41",
    "61",
    "89",
    "101",
    "643",
    "1361",
    "3491",
    "6091",
    "87049"
  ],
  "discriminant": "463541515935750417518113098687641441640539948171759286937537434489666615895631124560216256000000",
  "regulator": "942031705578444.3433585981304697090534852570755731138135504864006",
  "points": [
    [
      "-6685244291066",
      "11373031702830608827148"
    ],
    [
      "-3088886477780425055/2304",
      "-16964060301495901701616519025/110592"
    ],
    [
      "1113926190754693030/9",
      "1174925120567678344989109700/27"
    ],
    [
      "-12355545911121700220/33489",
      "-515962527706177138397991232900/6128487"
    ],
    [
      "637326309322684368409/2704",
      "-16086706177688691870266035208323/140608"
    ],
    [
      "507883368159829270/81",
      "257942570864429461262473900/729"
    ],
    [
      "50390034811827670",
      "-11268238228933783941637900"
    ],
    [
      "-143134500408212114780/32761",
      "199622478750220376880505105300/5929741"
    ],
    [
      "-572165430599501760132650/150822961",
      "253987795014603580978122982191338900/1852256784041"
    ],
    [
      "710104289787079453750/28561",
      "-18624213615344080555467798851500/4826809"
    ],
    [
      "-3418489052792751770/841",
      "-2613721914191026499926866500/24389"
    ],
    [
      "-2763470101327732775/5476",
      "39776970522721584576053409725/405224"
    ],
    [
      "26439644613419305/4",
      "3209032577947349933896075/8"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + a x with a = -19348006334886975416600173605900. 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 21:30:21",
  "updated_at": "2026-10-20 21:30:21"
}