{
  "id": 5101,
  "curve_key": "103861296:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-2163777",
    "0"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 55.375700623916444,
  "faltings_height": 2.682882130301194,
  "conductor": "149821788983328",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "19",
    "29"
  ],
  "discriminant": "648361882201957019712",
  "regulator": "195.6184165092622517504150871774905791737940326",
  "points": [
    [
      "-1463",
      "5852"
    ],
    [
      "-825",
      "34980"
    ],
    [
      "1596",
      "24738"
    ],
    [
      "3591",
      "196308"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5100: https://elliptic-rank.icarm.cloud/curve/5100. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (4,8,12,20), 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. Four rational points checked exactly; PARI/GP returned rank bounds [4,4]. Rational torsion C2.",
  "created_at": "2026-10-21 02:47:52",
  "updated_at": "2026-10-21 02:47:52"
}