{
  "id": 4904,
  "curve_key": "-27122363692224:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "565049243588",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 92.7941391959872,
  "faltings_height": 5.801085344640423,
  "conductor": "638561295358741918227488",
  "bad_primes": [
    "2",
    "41",
    "769",
    "2081",
    "2153"
  ],
  "discriminant": "-11546194461664978431928007811499102208",
  "regulator": "2294771375.45046611941559249506367199470323422854298896",
  "points": [
    [
      "290521/4",
      "-1628207427/8"
    ],
    [
      "1926544/9",
      "9763527896/27"
    ],
    [
      "20967241/144",
      "-504864316603/1728"
    ],
    [
      "4037204521/1444",
      "265629688166283/54872"
    ],
    [
      "362407369/36",
      "-6918356045989/216"
    ],
    [
      "23495984656/203401",
      "-23711632631850888/91733851"
    ],
    [
      "105925264/289",
      "-2487464608296/4913"
    ],
    [
      "227862067801/318096",
      "-157666623475023197/179406144"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4759, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4759.\r\n\r\nThe original curve y^2 = x^3 - 141262310897*x appears as the rank-8 example in Table 2, Section 6.1, of Julián Aguirre, Álvaro Lozano-Robledo and Juan Carlos Peral, Elliptic curves of maximal rank: https://alozano.clas.uconn.edu/wp-content/uploads/sites/490/2014/01/ALP-2-23-07.pdf.\r\n\r\nApplied the standard degree-2 isogeny with kernel generated by (0,0), sending y^2 = x^3 + A*x to y^2 = x^3 - 4*A*x. Here A = -141262310897, giving y^2 = x^3 + 565049243588*x. The coordinate map is X = (x^2+A)/x, Y = y*(x^2-A)/x^2.\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 638561295358741918227488. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:38:01",
  "updated_at": "2026-10-20 22:38:01"
}