{
  "id": 5079,
  "curve_key": "44004086191296:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-916751795652",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 94.24591084055653,
  "faltings_height": 5.922066315021202,
  "conductor": "373526157702740607157824",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "23",
    "59",
    "101",
    "127"
  ],
  "discriminant": "49310031714765059930905710167181299712",
  "regulator": "1725520.238424913546400846296206119176298755477838397",
  "points": [
    [
      "-309396",
      "504006084"
    ],
    [
      "2552517",
      "3780277677"
    ],
    [
      "4519872",
      "9391164048"
    ],
    [
      "-1730563700/1849",
      "15528647232820/79507"
    ],
    [
      "-4189059/25",
      "48235817511/125"
    ],
    [
      "129860346/25",
      "1454483097144/125"
    ],
    [
      "171869478/49",
      "2167617856536/343"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5078: https://elliptic-rank.icarm.cloud/curve/5078. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (12,15,31,36), 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. Seven rational points checked exactly; PARI/GP returned rank bounds [7,7]. Rational torsion C2.",
  "created_at": "2026-10-21 02:17:21",
  "updated_at": "2026-10-21 02:17:21"
}