{
  "id": 32,
  "curve_key": "163917537878828567281:-1263721367114133797432399098825",
  "ainvs": [
    "1",
    "0",
    "0",
    "-3414948705808928485",
    "1462640470912335058581199361"
  ],
  "rank_lower_bound": 10,
  "naive_height": 139.6376854723492,
  "faltings_height": 9.677832038105548,
  "conductor": "929053397624034727388941088597323782",
  "bad_primes": [
    "2",
    "3",
    "17",
    "19",
    "23",
    "29",
    "31",
    "37",
    "43",
    "47",
    "53",
    "59",
    "281",
    "74177",
    "4756942171609"
  ],
  "discriminant": "1624596034552120480493303406632087249542571198120190723072",
  "regulator": "347100868.2553289242017767590904381615260046941546101545684",
  "points": [
    [
      "1651118138",
      "18038584222223"
    ],
    [
      "1588614902",
      "6839177749439"
    ],
    [
      "-1189653814",
      "-61979712512809"
    ],
    [
      "-700495294",
      "-59253910115977"
    ],
    [
      "-147325510",
      "-44300624514889"
    ],
    [
      "11898974402",
      "1282784596947959"
    ],
    [
      "448355771899346/126025",
      "8290865418217263800429/44738875"
    ],
    [
      "-621829360",
      "-57841818977839"
    ],
    [
      "1692223027970/841",
      "1276149459553975651/24389"
    ],
    [
      "-380499314",
      "-52028047503377"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Found by Kretschmer (1986). A curve of rank exactly 10, via Dujella's elliptic-curve rank-records tables.",
  "created_at": "2026-05-27 22:12:11",
  "updated_at": "2026-07-01 22:51:30"
}