{
  "id": 5217,
  "curve_key": "348591936:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-7262332",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 59.00823767475754,
  "faltings_height": 2.9855935512046186,
  "conductor": "105482932156448",
  "bad_primes": [
    "2",
    "7",
    "11",
    "17",
    "19",
    "73"
  ],
  "discriminant": "24513666356915242135552",
  "regulator": "640.033719836462018120949235638353914690423475154",
  "points": [
    [
      "-2142",
      "75684"
    ],
    [
      "-1606",
      "86724"
    ],
    [
      "-1022",
      "79716"
    ],
    [
      "-374",
      "51612"
    ],
    [
      "30514",
      "5309436"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5216: https://elliptic-rank.icarm.cloud/curve/5216. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (4,7,12,14), 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. Five rational points checked exactly; PARI/GP returned rank bounds [5,5]. Rational torsion C2.",
  "created_at": "2026-10-21 10:23:30",
  "updated_at": "2026-10-21 10:23:30"
}