{
  "id": 5238,
  "curve_key": "-417094501824:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "8689468788",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 80.26973596844765,
  "faltings_height": 4.757385075678795,
  "conductor": "16779303959472486432",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "59",
    "61",
    "67"
  ],
  "discriminant": "-41991332555577884485137835511808",
  "regulator": "53156.36711646379883269099189319490139822263749481679",
  "points": [
    [
      "7198",
      "7932196"
    ],
    [
      "8437",
      "8597303"
    ],
    [
      "17446",
      "12526228"
    ],
    [
      "28548",
      "16472196"
    ],
    [
      "39589",
      "20150801"
    ],
    [
      "64782",
      "28892772"
    ],
    [
      "356301",
      "219837717"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5237: https://elliptic-rank.icarm.cloud/curve/5237. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (10,13,18,19), 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. Seven rational points checked exactly; PARI/GP returned rank bounds [7,7]. Rational torsion C2.",
  "created_at": "2026-10-21 10:51:42",
  "updated_at": "2026-10-21 10:51:42"
}