{
  "id": 526,
  "curve_key": "-5155337898078607385400343497539847880117488479:-3649946544007544955702544190608646414804204638708450906441754438675569",
  "ainvs": [
    "1",
    "0",
    "0",
    "107402872876637653862507156198746830835781010",
    "4224475166675399254285361022703117514716762429657056963210155804292"
  ],
  "rank_lower_bound": 17,
  "torsion": [
    2
  ],
  "naive_height": 320.34616787719784,
  "faltings_height": 24.75480047110181,
  "conductor": "896646894085414738018884578533457083277325095657891101842582783442629320910",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "53",
    "61",
    "107",
    "139",
    "167",
    "229",
    "281",
    "463",
    "491",
    "587",
    "877",
    "1399",
    "1423",
    "2099",
    "2591",
    "3851",
    "4129",
    "6421",
    "7369",
    "7417",
    "34303",
    "587413"
  ],
  "discriminant": "-7788845956417443911554322278168134310294674003014547938309309575453945390838340363818467939827696940904643050116642469355103174656000000",
  "regulator": "2636742048426089067919863.66574613493253502124361544397742051826238595793",
  "points": [
    [
      "-3761780732802174685862877684/299209",
      "154133708956120498730798871827429755609974/163667323"
    ],
    [
      "2495150654599314112273816224/1207801",
      "2801723577767260970148696186264239812371162/1327373299"
    ],
    [
      "7236342444903426893422533244956/49182169",
      "19527188493178507103674125021074069982942638586/344914551197"
    ],
    [
      "79011304842620331736185055656/508369",
      "22271031337869520773394676411145762644527986/362467097"
    ],
    [
      "3412512168014431686263886661952598492/2799287033449",
      "6304164137163291246087488459597691249359250993491550678/4683506730672756043"
    ],
    [
      "14733067881848492130956412628806556/254866454649",
      "1835955309628010954314988065178392877369751164528806/128667545564365107"
    ],
    [
      "445426823641567222882703973048/582169",
      "297307889363175791523068213213648523755438226/444194947"
    ],
    [
      "95773541100153994221846293875386/277455649",
      "937748214213890889523914919657725562062386014854/4621578745393"
    ],
    [
      "103412599381077506056053514400834685196316/5196879063984274969",
      "44708001123296815860915620805349465670200548981700005307820474/11847150779312927142608515453"
    ],
    [
      "-3036564086541812289781941749831724700164/293152354096798849",
      "224500353473404608576053379991947732946769758444734888981954/158723078811026107045388993"
    ],
    [
      "398508456053080731781071996924984/695324161",
      "7956685151686935029433521885834051173511689934022/18335002801409"
    ],
    [
      "33620910308209498670379354498204/222337921",
      "195522014634016413474177807642905638677075075678/3315280740031"
    ],
    [
      "-72519749011202448198365672644614369077891652/58105995124594852231729",
      "28321266369832639248338415796526239881556215685820929742067592912110/14006557709602424186191243506500183"
    ],
    [
      "-50097934008999194587954403602316102439/3704865703641664",
      "123436519520236967908284941932665813216650377370351985081/225506313341904976819712"
    ],
    [
      "25087654751338468512443484/841",
      "142156620745291157391934390906869054282/24389"
    ],
    [
      "-836317223593929460453632306836729871684/67474505856653809",
      "17431688731966755260197124973648973669230311861542669305426/17527080005714418847778377"
    ],
    [
      "-753714659100004438091452920433870634244/199288260207276769",
      "172606670313003313662438767540650598103927204206527810537314/88965694559443521783590353"
    ]
  ],
  "submitter": "Matthias Breddin",
  "history": [],
  "commentary": "Exact rank 17, unconditional: rational 2-torsion point, 17 independent points (Neron-Tate height matrix of rank 17; the archived certificate additionally saturates the lattice at all primes up to 97 — the points listed here are the ellrank output, not the saturated basis) with matching 2-descent upper bound 17 (PARI/GP 2.15.4 ellrank, effort 2). Fiber t=-622/2197 on branch u=82/37 of the Elkies-Klagsbrun Z/2Z rank-9 family (arXiv:2003.00077), found by a Mestre-Nagao residue-table sieve followed by an exact 2-descent-type upper bound and ellrank (Matthias Breddin, 2026-09-02; method: doi:10.5281/zenodo.22242107).",
  "created_at": "2026-09-02 13:43:21",
  "updated_at": "2026-09-02 13:43:21"
}