{
  "id": 31,
  "curve_key": "98918170715321792161:-896711378899860072200428904305",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2060795223235870670",
    "1037860392073475481628988676"
  ],
  "rank_lower_bound": 10,
  "naive_height": 138.12247387142565,
  "faltings_height": 9.477932235718134,
  "conductor": "240767746179482941231124244768162",
  "bad_primes": [
    "2",
    "3",
    "17",
    "19",
    "23",
    "29",
    "31",
    "37",
    "41",
    "43",
    "47",
    "53",
    "697675341112349"
  ],
  "discriminant": "94793787423403087849353656317664770631480997068191076352",
  "regulator": "17736686.04120010720386049179366267873878228181167867826206",
  "points": [
    [
      "150913924",
      "27023891033530"
    ],
    [
      "1309368796",
      "24172933593538"
    ],
    [
      "1714332274",
      "50430125403496"
    ],
    [
      "1088122156",
      "9154278492706"
    ],
    [
      "1080521116",
      "8523778305538"
    ],
    [
      "1048497604",
      "5456990794690"
    ],
    [
      "153591884988",
      "60191191934061474"
    ],
    [
      "1028141818",
      "2427298113664"
    ],
    [
      "1023547336",
      "925461825238"
    ],
    [
      "-1104208292",
      "-44351144023742"
    ]
  ],
  "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 22:12:10",
  "updated_at": "2026-07-01 22:51:29"
}