{
  "id": 5089,
  "curve_key": "-8302859285630906304:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "172976235117310548",
    "0"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 130.6893948648487,
  "faltings_height": 8.959023317045549,
  "conductor": "135695137938136502727507141369888",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "19",
    "23",
    "31",
    "43",
    "47",
    "107",
    "179"
  ],
  "discriminant": "-331237344997119260553454130311763417072176291282341888",
  "regulator": "128250274.35784558829848034060348460968737260603487785102",
  "points": [
    [
      "242422992",
      "7495355278152"
    ],
    [
      "2106388944",
      "98540034383736"
    ],
    [
      "2796217732",
      "149488596170452"
    ],
    [
      "6955902052",
      "581172572346652"
    ],
    [
      "103213058256",
      "33159310832434248"
    ],
    [
      "2854122601/16",
      "386827798481333/64"
    ],
    [
      "2956312737/256",
      "5791295442960783/4096"
    ],
    [
      "3833313561/4",
      "258721832172573/8"
    ],
    [
      "3833313561/16",
      "475472714165757/64"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (9,27,29,41), 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. Nine rational points checked exactly; PARI/GP returned rank bounds [9,9]. Rational torsion C2.",
  "created_at": "2026-10-21 02:28:31",
  "updated_at": "2026-10-21 02:28:31"
}