{
  "id": 5086,
  "curve_key": "-25045212062211264:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "521775251296068",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 113.27837720679547,
  "faltings_height": 7.508105178874446,
  "conductor": "544498825730149822227584521248",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "29",
    "31",
    "43",
    "59",
    "83",
    "157"
  ],
  "discriminant": "-9091392372024411523093673288485328873115291648",
  "regulator": "4251937.00515022356226059052829892751674803117553030968",
  "points": [
    [
      "754138",
      "19847403884"
    ],
    [
      "3127476",
      "40772904612"
    ],
    [
      "43263418",
      "321793303084"
    ],
    [
      "139105344",
      "1662621847824"
    ],
    [
      "166835893/81",
      "23995505982511/729"
    ],
    [
      "268688596/49",
      "18868119276908/343"
    ],
    [
      "667343572/9",
      "18038964094732/27"
    ],
    [
      "691882986/625",
      "375965063294484/15625"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (3,10,18,27), 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. Eight rational points checked exactly; PARI/GP returned rank bounds [8,8]. Rational torsion C2.",
  "created_at": "2026-10-21 02:25:52",
  "updated_at": "2026-10-21 02:25:52"
}