{
  "id": 4962,
  "curve_key": "419076124763814801:-912951921235352198434447545",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-8730752599246142",
    "1056657318427308749851405"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 124.15745090172645,
  "faltings_height": 8.401267397775033,
  "conductor": "2279229518497181053800334368402",
  "bad_primes": [
    "2",
    "3",
    "23",
    "29",
    "31",
    "37",
    "41",
    "61",
    "193",
    "281",
    "8893",
    "18181",
    "203977"
  ],
  "discriminant": "-439745978346996453774003144365949860616230481004608",
  "regulator": "153947042462.828253736482991122193519371166634554521985763960",
  "points": [
    [
      "-90616007",
      "1050631616507"
    ],
    [
      "188375263",
      "2469023233187"
    ],
    [
      "-121500155",
      "569116865039"
    ],
    [
      "176500015",
      "2239119837059"
    ],
    [
      "162486205",
      "-1981987733605"
    ],
    [
      "-90390125",
      "1052333150369"
    ],
    [
      "48871033",
      "864092982299"
    ],
    [
      "1611895993",
      "64613633384507"
    ],
    [
      "-32570724125/289",
      "3834729786512065/4913"
    ],
    [
      "-3161462549/25",
      "-46501858203539/125"
    ],
    [
      "-13005587",
      "1080749787287"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4899, submitted by Ritik Jain: https://elliptic-rank.icarm.cloud/curve/4899.\r\n\r\nThe source model is y^2 + x*y + y = x^3 - x^2 - 13629998356645502*x + 611263221986306397530125. Its public entry supplies eleven rational points and no commentary identifying an earlier source.\r\n\r\nApplied the degree-2 isogeny with kernel generated by the rational order-2 point (64936249, -32468125), then converted the target to its minimal model y^2 + x*y + y = x^3 - x^2 - 8730752599246142*x + 1056657318427308749851405.\r\n\r\nEleven 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 2279229518497181053800334368402. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:56:27",
  "updated_at": "2026-10-20 23:56:27"
}