{
  "id": 6261,
  "curve_key": "6608655625038944025:-17336369421249647754301177725",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-137680325521644667",
    "20065242420125692207148641"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 130.04520816866454,
  "faltings_height": 8.732996811302005,
  "conductor": "1890078571877413719648273191875440370070885076550",
  "bad_primes": [
    "2",
    "5",
    "73",
    "61187353391173",
    "8463019186486703731252092008039"
  ],
  "discriminant": "-6898786787352560076716197150345357350758730529407500",
  "regulator": "366148311652021.906941870117484656489456530090539188108402759472634836584",
  "points": [
    [
      "4455663149/16",
      "-116628757248093/64"
    ],
    [
      "763679444179",
      "-667370258975633782"
    ],
    [
      "69546973906/225",
      "-8955528126455891/3375"
    ],
    [
      "1912966569031/324",
      "-2640741091511965469/5832"
    ],
    [
      "220952335401/1024",
      "20811333777462299/32768"
    ],
    [
      "-11054446784/1089",
      "-166484696366970479/35937"
    ],
    [
      "308266714011/1444",
      "-34810502354298949/54872"
    ],
    [
      "4511618423349/1936",
      "9468272905436929427/85184"
    ],
    [
      "9081398219751/2500",
      "27229502259070904099/125000"
    ],
    [
      "137366125",
      "1935041945121"
    ],
    [
      "190516114",
      "865912199723"
    ],
    [
      "210666450",
      "640260517979"
    ],
    [
      "218057554",
      "641332412603"
    ],
    [
      "269501384",
      "1591831965463"
    ],
    [
      "1630826871/4",
      "45042705110339/8"
    ],
    [
      "790146728",
      "20114061247713"
    ],
    [
      "-3702700304/9",
      "71814236156491/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 17 proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file mestre/mestre_rank_17.tsv.gz:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-10-31 23:18:45",
  "updated_at": "2026-10-31 23:18:45"
}