{
  "id": 4963,
  "curve_key": "5973727649701049443161:-461658303829046047040891604613341",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-124452659368771863399",
    "534326740573990534102484174893"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 150.42497424707898,
  "faltings_height": 10.233848944948488,
  "conductor": "3368735979785622317933377456962690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "23",
    "53",
    "73",
    "131",
    "193",
    "277",
    "293",
    "479",
    "1993",
    "3373",
    "7207"
  ],
  "discriminant": "26969209660571985036102258623226693939106622620785770250000",
  "regulator": "65445889773943.593466463270755935719075226344667583837563548351",
  "points": [
    [
      "21798904218",
      "-2860092181369859"
    ],
    [
      "222476568711/25",
      "-45339732812439949/125"
    ],
    [
      "16500152802407673/43264",
      "-2118597809632250991705467/8998912"
    ],
    [
      "8848949882",
      "354902331948509"
    ],
    [
      "415957290273/64",
      "-1443489197112317/512"
    ],
    [
      "45144787332548022/6880129",
      "270813557254093532098667/18046578367"
    ],
    [
      "75281792348698/1089",
      "645155548092492327133/35937"
    ],
    [
      "6554344118",
      "-13861527794539"
    ],
    [
      "20687686682",
      "2610279511555709"
    ],
    [
      "29348098682",
      "4707395971997609"
    ],
    [
      "450397138417967/69169",
      "-113053374356205159623/18191447"
    ],
    [
      "576811341838314503/61795321",
      "209459713539100450639805066/485773018381"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4649, submitted by Andrii Prokhorenkov: https://elliptic-rank.icarm.cloud/curve/4649.\r\n\r\nThe source commentary identifies X720. The source model is y^2 + x*y = x^3 - x^2 - 135106943487621085899*x + 437436449661005173548681415393. No specialization parameter is given in the commentary.\r\n\r\nApplied a rational degree-2 isogeny and converted the target to its minimal model y^2 + x*y = x^3 - x^2 - 124452659368771863399*x + 534326740573990534102484174893.\r\n\r\nTwelve supplied rational points transported through this map and checked exactly on the target curve. Rational torsion Z/2Z. Same rank and conductor as the source; conductor 3368735979785622317933377456962690. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:57:43",
  "updated_at": "2026-10-20 23:57:43"
}