{
  "id": 5277,
  "curve_key": "-2953130995584:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "61523562408",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 86.14166123363137,
  "faltings_height": 5.246712181110771,
  "conductor": "15140594925484283033856",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "23",
    "29",
    "37",
    "71"
  ],
  "discriminant": "-14904053388676486349705203086163968",
  "regulator": "186305.0328769135055725118876131057965742856748496633",
  "points": [
    [
      "47656",
      "55137992"
    ],
    [
      "61161",
      "63179313"
    ],
    [
      "82593",
      "75132099"
    ],
    [
      "151848",
      "113329224"
    ],
    [
      "762496",
      "700161952"
    ],
    [
      "2129064",
      "3127595016"
    ],
    [
      "172753/9",
      "930620411/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5276: https://elliptic-rank.icarm.cloud/curve/5276. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (3,4,6,10), reduced by rational fourth-power scaling. Reference: “High rank elliptic curves with torsion group Z/(2Z),” Math. Comp. 73 (2004), 323–331, doi:10.1090/S0025-5718-03-01547-3.",
  "created_at": "2026-10-21 11:52:22",
  "updated_at": "2026-10-21 11:52:22"
}