{
  "id": 5504,
  "curve_key": "2520571725071252276978736:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-52511910938984422437057",
    "0"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 168.55958394802937,
  "faltings_height": 12.114872407310605,
  "conductor": "58014480798713096047867061716102842721931808",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "19",
    "23",
    "53",
    "113",
    "131",
    "139",
    "277",
    "307",
    "1217"
  ],
  "discriminant": "9267304699073016530129498448259956823322414350510376364215180327948352",
  "regulator": "21528995256546643.4680474807191203527600314156490930619944245",
  "points": [
    [
      "757946552172385081/3073009",
      "244067934924661018254846092/5386984777"
    ],
    [
      "436045015640680209/687241",
      "268501415170243596324279876/569722789"
    ],
    [
      "619180057285762401/1243225",
      "-432584411954856857016559524/1386195875"
    ],
    [
      "57765906974942881/21025",
      "13835394462396135213967096/3048625"
    ],
    [
      "38140301463567241/17161",
      "-7408927207752180167149912/2248091"
    ],
    [
      "9995272632232248374689/15475111201",
      "934284151005191501560827253923464/1925088358293199"
    ],
    [
      "127872541238846209/399424",
      "31931368750265400258030721/252435968"
    ],
    [
      "640975144056223743617439681/1993616695504225",
      "11382741836701077992982466834179885655296/89014855869178438475375"
    ],
    [
      "121219171913435251378969/514926864",
      "42204306034714840535869087766805629/11684720397888"
    ],
    [
      "6616769543765642968635174129/15109211347099024",
      "-458663444186760139255187390971565397294519/1857217187674501587736768"
    ],
    [
      "53267762490138731281491380919361/190534548356269057600",
      "-222704364463457618476974838240330509592798316641/2630029393872924821906853824000"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of a curve from my own run at tuple (11,23,29,50). (capture APH-07f1610bc9cb7d3079b579ba). For y^2 = x^3 + A*x, the partner is y^2 = x^3 - 4*A*x. I transported the 11 stored points by (x,y) -> (x + A/x, y*(1 - A/x^2)); each image checks exactly on the partner.",
  "created_at": "2026-10-22 19:09:18",
  "updated_at": "2026-10-22 19:09:18"
}