{
  "id": 3968,
  "curve_key": "51276651246589781318241021193:3592702486468489338771954233531365750745755",
  "ainvs": [
    "1",
    "1",
    "0",
    "-1068263567637287110796687941",
    "-4158220470450085548213314417698208979635"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2,
    2
  ],
  "naive_height": 198.32109905404698,
  "faltings_height": 14.588909197091532,
  "conductor": "1321043258541830079458759813032686",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "17",
    "43",
    "101",
    "131",
    "179",
    "509",
    "587",
    "1367",
    "2141",
    "13217",
    "120917"
  ],
  "discriminant": "70552042644207985438560994076801910596606186261102474837966356990503199580610572544",
  "regulator": "249811848849671.7137689628501406653838830920108058812197360",
  "points": [
    [
      "49563369211885905146/49729",
      "-348743945339319266212674356539/11089567"
    ],
    [
      "-16353069938539745542334271029831/1628113262236373056",
      "154880953943729073627275233202978460381420061583/2077432497077173200460791296"
    ],
    [
      "1544103711018156298672139/23665207225",
      "-1643968837321130290538921963628969058/3640537153457875"
    ],
    [
      "83600137357801813026490/2719201",
      "-24171869577616045988823356306936485/4483962449"
    ],
    [
      "-86047340361524465999/6471936",
      "-1444256844509680425220694779777/16464605184"
    ],
    [
      "1061330483836428125551786/24043913721",
      "694447437978297787476347892978812767/3728273305491981"
    ],
    [
      "98947801358600335321665398554/109624773934225",
      "-31104489694034515291987822518103302637219837/1147791663674513581625"
    ],
    [
      "9443196242910326862740025139319151241210/88933484003888866055258689",
      "871421817816451509150451831161431456243869927031939359308485/838683230665175189221964334966806025887"
    ],
    [
      "34840459933731240790318953541932641/434072945063915982400",
      "-5910882482298535088822238273440940679166503722824749/9043656884783059650739375168000"
    ],
    [
      "31405622457658425136215080315/643835257940281",
      "3994865105285018833076739848442772252297090/16336617245968217528429"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3698 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 10: 10 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 04:36:21",
  "updated_at": "2026-10-05 04:36:21"
}