{
  "id": 5080,
  "curve_key": "-16373785904784:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "341120539683",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 91.28010825444547,
  "faltings_height": 5.674916099511946,
  "conductor": "8443589848063214711328",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "41",
    "233",
    "433"
  ],
  "discriminant": "-2540408658584903369221995148820799168",
  "regulator": "47913796.55089484200882600524896576217027165596660097",
  "points": [
    [
      "1683413424",
      "69069482994204"
    ],
    [
      "6273/4",
      "185034681/8"
    ],
    [
      "36108081/289",
      "1037218886082/4913"
    ],
    [
      "1764302857/35721",
      "879450687802142/6751269"
    ],
    [
      "37902282187/822649",
      "93831420414087818/746142643"
    ],
    [
      "963198708571/4923961",
      "2976548616283454542/10926269459"
    ],
    [
      "195483113977536/100741369",
      "2854273982943484869768/1011141120653"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (6,18,20,52), 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. Selected in a bounded tuple search using a small-prime sieve and height screening, following the search approach described by David Renshaw on https://elliptic-rank.icarm.cloud/curve/4986. Seven rational points checked exactly; PARI/GP returned rank bounds [7,7]. Rational torsion C2.",
  "created_at": "2026-10-21 02:18:35",
  "updated_at": "2026-10-21 02:18:35"
}