{
  "id": 3989,
  "curve_key": "12722488886253206897796496:-44770687957731402621089192878553227456",
  "ainvs": [
    "0",
    "1",
    "0",
    "-265051851796941810370760",
    "51817925876915587601587585228201908"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "naive_height": 173.41624031336107,
  "faltings_height": 12.329438362394525,
  "conductor": "11537416688626259646150573805118160",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "19",
    "59",
    "73",
    "101",
    "103",
    "107",
    "137",
    "179",
    "881",
    "1579",
    "1979",
    "2459"
  ],
  "discriminant": "31753169925766772256447566567759566054536835266391447159701326400000000",
  "regulator": "255283205572818499.71321602499427030020491999974780444210948799",
  "points": [
    [
      "783372909627574/2209",
      "-5108976562518116085600/103823"
    ],
    [
      "521071371666499529612854/355653598689",
      "-355443965010032551375080721698042400/212100069689362863"
    ],
    [
      "83827409094604305631/129709321",
      "-572994714450660754189604777550/1477259456869"
    ],
    [
      "3919815516218786998294/1439823025",
      "-241306046440834966932693372384672/54634084683625"
    ],
    [
      "12460616125791336026641/18626790400",
      "-1060050231505868725477038448048761/2542184353792000"
    ],
    [
      "11141064930659991169/1567504",
      "-37091912914529803923511235625/1962515008"
    ],
    [
      "18016473150249006406/25921",
      "-76472369863840623525203419200/4173281"
    ],
    [
      "50585218077903615193/66064384",
      "293025298278168466013308719645/536971313152"
    ],
    [
      "1459716945670901951907766/14266152481",
      "1763589431331118932420784622796223200/1703963518483121"
    ],
    [
      "472433743803845706947974/750990360409",
      "238263581189273943519154971267602400/650805993359358173"
    ],
    [
      "1376696428091920575100022614/3782599697082649",
      "-13883892619422722975062039239755878454400/232640635301521719471107"
    ],
    [
      "14778529530249273544922534136151591/2008488501088808618881",
      "1792295187055898467239884313539925841833845960344950/90012748833740728465299943585471"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3634 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 12: 12 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 04:40:35",
  "updated_at": "2026-10-05 04:40:35"
}