{
  "id": 5249,
  "curve_key": "774545887907814519072576:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-16136372664746135814012",
    "0"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 165.01969157821557,
  "faltings_height": 11.819881376492788,
  "conductor": "10627858072472094204174121166893361218593312",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "23",
    "31",
    "47",
    "53",
    "67",
    "83",
    "199",
    "251",
    "389"
  ],
  "discriminant": "268904283065170323529780116633648429721463863607513440474120169582592",
  "regulator": "41624158494.12960260592823494872155269337593272704107183244",
  "points": [
    [
      "-126737391326",
      "3062575058678044"
    ],
    [
      "-116520927302",
      "17268634468011004"
    ],
    [
      "-115145074316",
      "18204003462700964"
    ],
    [
      "422968268514",
      "262382853141031524"
    ],
    [
      "374305734783253",
      "7241686111799127886079"
    ],
    [
      "-9506280126251/81",
      "12139211389446060191/729"
    ],
    [
      "-2464330016876/81",
      "15682307229718263316/729"
    ],
    [
      "5229225804594/25",
      "9500220351566871828/125"
    ],
    [
      "30860691554368/49",
      "167915237001935313904/343"
    ],
    [
      "157343106240853/841",
      "1448989714430967781631/24389"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (5,14,19,21), 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 following the parametrization search described by David Renshaw on https://elliptic-rank.icarm.cloud/curve/4986. Ten rational points checked exactly; PARI/GP returned rank bounds [10,10]. Rational torsion C2.",
  "created_at": "2026-10-21 11:08:03",
  "updated_at": "2026-10-21 11:08:03"
}