{
  "id": 4941,
  "curve_key": "-10283604912:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "214241769",
    "0"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 69.16145012362736,
  "faltings_height": 3.8316945886104365,
  "conductor": "13711473216",
  "bad_primes": [
    "2",
    "3",
    "7",
    "17",
    "41"
  ],
  "discriminant": "-629350252790274024816614976",
  "regulator": "2764.672501466871728932331803378789625846240685",
  "points": [
    [
      "41616",
      "8999460"
    ],
    [
      "1625625/676",
      "12784760325/17576"
    ],
    [
      "5035536/529",
      "20726380620/12167"
    ],
    [
      "471951138169/25600",
      "324224398746623053/4096000"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #15, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/15.\r\n\r\nThe source commentary attributes the original curve y^2 = x^3 - 856967076*x to Wiman (1945), via Dujella's elliptic-curve rank-record tables.\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 = -856967076, the combined map is X = (x^2+A)/(4*x), Y = y*(x^2-A)/(8*x^2), giving y^2 = x^3 + 214241769*x.\r\n\r\nFour 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 13711473216. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:24:50",
  "updated_at": "2026-10-20 23:24:50"
}