{
  "id": 3834,
  "curve_key": "-2038035387294634928480638915045403123039:-103577525525863089770604441485701257568776197502211478045041",
  "ainvs": [
    "1",
    "0",
    "0",
    "42459070568638227676679977396779231730",
    "119881395284563761312108211303985196714695782262476368900"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    6
  ],
  "naive_height": 271.77534134374724,
  "faltings_height": 20.761059763348108,
  "conductor": "11562784654375022501788319763332764230",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "29",
    "37",
    "43",
    "67",
    "113",
    "419",
    "421",
    "677",
    "4639",
    "52081",
    "87421"
  ],
  "discriminant": "-11107328478678772403490795196964524119060281489563172850238608426157217313471108866721347959826585379493933056000000",
  "regulator": "498533387.67651568063263206019866626901031222099685486300",
  "points": [
    [
      "-31033395220068260",
      "-10888696720875752056116741470"
    ],
    [
      "-1232864448860804240",
      "-8103161016824343141105844670"
    ],
    [
      "-1328315624621856260",
      "-7819120064970281438189301470"
    ],
    [
      "3802553855770780126",
      "18338947764785709323657418652"
    ],
    [
      "-2433590726687000900",
      "-1463142233956860582883774430"
    ],
    [
      "3867651990684847612",
      "18491984028573822481136771362"
    ],
    [
      "-1218313370645706530",
      "-8145220354674240158153680250"
    ],
    [
      "-1878910201911913560",
      "-5785455130632454988224496970"
    ],
    [
      "28632932208035602735/4",
      "224941354774375071659805792365/8"
    ]
  ],
  "submitter": "dujella",
  "history": [],
  "commentary": "Found within the two-parameter family by Dujella-Peral, y² = x³ + (1 + 6t − 3t²)x² − 16t³x, t = v(w² − 1)/((v + 1)(4v − w² + 1)), at v = 1/6 and w = 112741/62861. The curve was found with the assistance of Claude, based on our old PARI/GP program.",
  "created_at": "2026-10-03 06:59:59",
  "updated_at": "2026-10-03 06:59:59"
}