{
  "id": 4002,
  "curve_key": "25207507943905298659271623064641:-126488512432498376288455973770440609715556794465",
  "ainvs": [
    "1",
    "0",
    "0",
    "-525156415498027055401492147180",
    "146398741241317521385641270732051644453845136"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2
  ],
  "naive_height": 216.9140840227413,
  "faltings_height": 15.828928375625308,
  "conductor": "304327139592757069203804262254572708025894",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "19",
    "41",
    "53",
    "59",
    "97",
    "113",
    "157",
    "251",
    "271",
    "373",
    "431",
    "1471",
    "1523",
    "5569",
    "67751"
  ],
  "discriminant": "10400473751702908114072334499083225541361676599920073935295178625147116347912157971698432",
  "regulator": "2408388679028026634.52120128114855798751596271404478265372964386968",
  "points": [
    [
      "2928819534860289849088/2461761",
      "-134112837988792328662073772336524/3862503009"
    ],
    [
      "7039841506762152848/10201",
      "-10935362462153182736761545116/1030301"
    ],
    [
      "349706028202300531808/654481",
      "-2267877342822636507069853065524/529475129"
    ],
    [
      "28567689591270472364/66049",
      "7024209237246875820798504784/16974593"
    ],
    [
      "41946974186528608/81",
      "2660748946142536652972876/729"
    ],
    [
      "611013394853738",
      "7323610146183644355104"
    ],
    [
      "1229455280401630086954584/298149289",
      "-1343458797094614845741325759641639156/5148143773163"
    ],
    [
      "4988242059013053551095625858/72012259201",
      "-352287804233169507357779453172197779689886/19324561768847551"
    ],
    [
      "185135797838665877498/373321",
      "-642219187069417426762587260576/228099131"
    ],
    [
      "204389428392956704/225",
      "69079974931227700039232212/3375"
    ],
    [
      "48075655317356815534/8649",
      "330638543577252647087275971472/804357"
    ],
    [
      "128191434702313881152/267289",
      "304304741057565928985496905372/138188413"
    ],
    [
      "22539475977120707244686/51825601",
      "-191975129613409864388923013757026/373092501599"
    ],
    [
      "12970536073932458069309354/30180375625",
      "-1498416466414872844834161583353863008/5243085755453125"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3640 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 14: 14 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.",
  "created_at": "2026-10-05 04:43:30",
  "updated_at": "2026-10-05 04:43:30"
}