{
  "id": 4907,
  "curve_key": "-177029921540304:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "3688123365423",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 98.42201964739691,
  "faltings_height": 6.270075382257899,
  "conductor": "48363569630503379882556192",
  "bad_primes": [
    "2",
    "3",
    "7",
    "23",
    "71",
    "113",
    "281",
    "1129"
  ],
  "discriminant": "-3210674601411390996180528791957052285888",
  "regulator": "78649085311.3971645931432292787981615694350125091197828",
  "points": [
    [
      "5827948281/14884",
      "2227022416078587/1815848"
    ],
    [
      "161315401",
      "2049012093232"
    ],
    [
      "26988246961/8464",
      "5175712040512663/778688"
    ],
    [
      "8322226941091734441/5419574688004",
      "38443634540342438760618517197/12616759034523935992"
    ],
    [
      "563931400969302921/490030800484",
      "823878093552287911179392547/343032341016410648"
    ],
    [
      "24805489821121/3888784",
      "129021816444391707103/7668682048"
    ],
    [
      "13067004721/9",
      "1493703683351272/27"
    ],
    [
      "3903137745159409/1029383056",
      "273342139953549709229641/33026725968704"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4762, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4762.\r\n\r\nThe source commentary attributes the original curve y^2 = x^3 - 14752493461692*x to Aguirre, Castañeda and Peral, High rank elliptic curves of the form y^2=x^3+Bx, Revista Matemática Complutense 13 (2000), 17–31: https://revistas.ucm.es/index.php/REMA/article/view/REMA0000120017A.\r\n\r\nApplied the standard degree-2 isogeny with kernel generated by (0,0), followed by the rational change of coordinates dividing x by 4 and y by 8. With A = -14752493461692, the combined map is X = (x^2+A)/(4*x), Y = y*(x^2-A)/(8*x^2), giving y^2 = x^3 + 3688123365423*x.\r\n\r\nEight supplied rational points transported through this map and checked exactly on the target curve. Rational torsion C2. Same rank and conductor as the source; conductor 48363569630503379882556192. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:42:35",
  "updated_at": "2026-10-20 22:42:35"
}