{
  "id": 4903,
  "curve_key": "-302793032064:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "6308188168",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 79.30894603970177,
  "faltings_height": 4.677319248283305,
  "conductor": "159172951851580784896",
  "bad_primes": [
    "2",
    "41",
    "2593",
    "7417"
  ],
  "discriminant": "-16065486904572409590033604968448",
  "regulator": "128134344.2467897666674060752330878106797078614871174",
  "points": [
    [
      "205209",
      "99679479"
    ],
    [
      "398161/9",
      "516301237/27"
    ],
    [
      "33721249/81",
      "199351075501/729"
    ],
    [
      "243079281/7225",
      "9716319478821/614125"
    ],
    [
      "1576963521/289",
      "62629431787293/4913"
    ],
    [
      "252354517801/42849",
      "126781567046228287/8869743"
    ],
    [
      "30880249/2025",
      "910078219943/91125"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4758, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4758.\r\n\r\nThe original curve y^2 = x^3 - 1577047042*x appears as the rank-7 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 = -1577047042, giving y^2 = x^3 + 6308188168*x. The coordinate map is X = (x^2+A)/x, Y = y*(x^2-A)/x^2.\r\n\r\nSeven 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 159172951851580784896. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:36:37",
  "updated_at": "2026-10-20 22:36:37"
}