{
  "id": 4906,
  "curve_key": "-198427744558421184:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "4133911344967108",
    "0"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 119.48760426452652,
  "faltings_height": 8.0255407670187,
  "conductor": "34178446016095527602163203767328",
  "bad_primes": [
    "2",
    "73",
    "673",
    "2129",
    "2393",
    "4129"
  ],
  "discriminant": "-4521301303657061014783414416045235438011041517568",
  "regulator": "3878975433020.677911034527664417488099736221914193397317631",
  "points": [
    [
      "229431609/16",
      "15964967945619/64"
    ],
    [
      "28057590016/441",
      "6681699853506208/9261"
    ],
    [
      "234179534241/128164",
      "3989297292365370897/45882712"
    ],
    [
      "433647273361/15876",
      "-730330367006421287/2000376"
    ],
    [
      "1922385023001/107584",
      "-9954146825706821757/35287552"
    ],
    [
      "20126375071911936/230037889",
      "-3543356454062120241022848/3488984662463"
    ],
    [
      "448352107281/19600",
      "-895627209097432071/2744000"
    ],
    [
      "6232756909401/329476",
      "55128056932004777853/189119224"
    ],
    [
      "651990036681/8836",
      "698274981263129307/830584"
    ],
    [
      "892737743104/441",
      "-843926811765268384/9261"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4763, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4763.\r\n\r\nThe original curve y^2 = x^3 - 1033477836241777*x appears as the rank-10 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 = -1033477836241777, giving y^2 = x^3 + 4133911344967108*x. The coordinate map is X = (x^2+A)/x, Y = y*(x^2-A)/x^2.\r\n\r\nTen 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 34178446016095527602163203767328. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:40:54",
  "updated_at": "2026-10-20 22:40:54"
}