{
  "id": 5702,
  "curve_key": "2661699494976:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-55452072812",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 85.82995782777937,
  "faltings_height": 5.22073689728977,
  "conductor": "6149864758294699174688",
  "bad_primes": [
    "2",
    "17",
    "19",
    "157",
    "461",
    "593"
  ],
  "discriminant": "10912727947549134066829929068244992",
  "regulator": "641520094.722072353034569630541225331880407638197116724",
  "points": [
    [
      "2292196/9",
      "-1322082332/27"
    ],
    [
      "5410276/9",
      "-11578590748/27"
    ],
    [
      "797836516/2601",
      "-14441378686948/132651"
    ],
    [
      "3667150249/900",
      "221700448757557/27000"
    ],
    [
      "169598529/484",
      "-1635601715199/10648"
    ],
    [
      "119727364/441",
      "-651969419156/9261"
    ],
    [
      "15832441/36",
      "-53205687917/216"
    ],
    [
      "116510436/121",
      "1219426222812/1331"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of Michael Rubinstein’s ICARM curve #5674:\r\nhttps://elliptic-rank.icarm.cloud/curve/5674\r\n\r\nRubinstein reports rank 8 proved, with eight independent points and a matching 2-descent upper bound, for the quartic twist y^2 = x^3 + 13863018203*x.\r\n\r\nWriting A = 13863018203, the rational 2-isogeny\r\n(x,y) -> (x + A/x, y*(x^2-A)/x^2)\r\ngives the global minimal model y^2 = x^3 - 55452072812*x.\r\n\r\nThe eight submitted points are the exact transported images of Rubinstein’s witnesses; each was checked on the destination curve. Rational isogeny preserves rank and independence modulo torsion. The destination has rational torsion Z/2Z and conductor 6149864758294699174688, equal to the source conductor.",
  "created_at": "2026-10-24 13:52:56",
  "updated_at": "2026-10-24 13:52:56"
}