{
  "id": 4993,
  "curve_key": "3788067696:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-78918077",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 66.16536564984803,
  "faltings_height": 3.5820208824621598,
  "conductor": "4067306368899872",
  "bad_primes": [
    "2",
    "7",
    "19",
    "29",
    "37",
    "79"
  ],
  "discriminant": "31456431725936189371042112",
  "regulator": "2468.24341508875373140039512738148290952776233590",
  "points": [
    [
      "-6004",
      "507338"
    ],
    [
      "-1501",
      "339226"
    ],
    [
      "-703",
      "234802"
    ],
    [
      "9164",
      "215354"
    ],
    [
      "36656",
      "6808852"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (14,28,32,34), 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. Five rational points checked exactly; PARI/GP returned rank bounds [5,5]. Rational torsion C2.",
  "created_at": "2026-10-21 01:34:05",
  "updated_at": "2026-10-21 01:34:05"
}