{
  "id": 5070,
  "curve_key": "6030551856:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-125636497",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 67.56031308571774,
  "faltings_height": 3.6982665021179684,
  "conductor": "505104940109792288",
  "bad_primes": [
    "2",
    "7",
    "29",
    "37",
    "43",
    "389"
  ],
  "discriminant": "126919230585578196923870272",
  "regulator": "19952.065512793386580675428096856905385636109037391",
  "points": [
    [
      "-11137",
      "133644"
    ],
    [
      "-7511",
      "721056"
    ],
    [
      "-175",
      "148260"
    ],
    [
      "11223",
      "59856"
    ],
    [
      "26825",
      "3991560"
    ],
    [
      "-368039/36",
      "100369493/216"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5067: https://elliptic-rank.icarm.cloud/curve/5067. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (18,22,50,54), 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. Points transported by the rational 2-isogeny and reduced with PARI/GP. Six rational points checked exactly; PARI/GP returned rank bounds [6,6]. Rational torsion C2.",
  "created_at": "2026-10-21 02:03:04",
  "updated_at": "2026-10-21 02:03:04"
}