{
  "id": 3471,
  "curve_key": "16805665636830139161554850324181014841:-68876446364003082579716070575695855338581129442125530861",
  "ainvs": [
    "1",
    "0",
    "1",
    "-350118034100627899199059381753771143",
    "79718109217596160364013393657928989116028766152608806"
  ],
  "rank_lower_bound": 16,
  "torsion": [
    2
  ],
  "naive_height": 257.14433825288893,
  "faltings_height": 19.155144756924663,
  "conductor": "44669319913005297558669849962700626503968806944547821921770",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "53",
    "67",
    "71",
    "103",
    "113",
    "139",
    "251",
    "283",
    "293",
    "353",
    "439",
    "1021",
    "1103",
    "1201",
    "3467",
    "3607",
    "23311",
    "35977",
    "54539"
  ],
  "discriminant": "1427061502949408209948821118859574534012152857371141880883530382263634308365095837836356405097865102620500",
  "regulator": "1441309252276395193898.852952436943026249415480591682880443113069876429",
  "points": [
    [
      "336723639306484325",
      "1939783285706651332429632"
    ],
    [
      "100304027013478586123/4",
      "1004286701102481817409869147839/8"
    ],
    [
      "-190796507246457898091087859949136755/1087765889089464649",
      "417970992072996486299306753849344584406146977250077376/1134496482463992637366989893"
    ],
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      "-253219474021160411940304675/1022784361",
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    ],
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      "16739931735380598108644/49729",
      "24232619716782336362131771853778/11089567"
    ],
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      "2101245384445273844417531/122899396",
      "369970822943236918935776359647890353869/1362462704056"
    ],
    [
      "2514610358438468694305720/7219969",
      "97149647057384817261055857514143171/19400056703"
    ],
    [
      "3407488916351076119572730/619369",
      "6255043086629375944835529993033211071/487443403"
    ],
    [
      "7954951877440925879234888/21187609",
      "3365669916052609678348374467220437358/97526564227"
    ],
    [
      "32485240982384442001628165/144024001",
      "191087418367187361090986365418119567482/1728432036001"
    ],
    [
      "177312097848877669212260005/587383696",
      "557967831424152034813695806109342142147/14235831256256"
    ],
    [
      "2193963036111735666495800789/6326611600",
      "1304063546948965494669122698229757490533/503218686664000"
    ],
    [
      "26077237932572393807597078005/77502662449",
      "54445719968455985141417012868476328344074/21576198707164457"
    ],
    [
      "144174552310166095669917472675/180704908836",
      "42648911383786447365265859463928269676258753/76816572516730584"
    ],
    [
      "1752306117849194400534791843555/5326674745681",
      "146174601811236960044569850471651230606927998/12293746919367175079"
    ],
    [
      "152658079389260696386403812537064/430575572599225",
      "110355956242832188115528607056606599925667954183/8934578762739287505875"
    ]
  ],
  "submitter": "Steps Unbounded",
  "history": [],
  "commentary": "Z/2Z curve from the Elkies-Klagsbrun rank-9 family y^2=x^3+2A(t,u)x^2+B(t,u)x (Elkies-Klagsbrun 2020), fibre u=2/5, t=-921/2080. Found by sweeping t=a/b with |a|,b<=8192 using the lossless conic-Hilbert prefilter of Breddin (Zenodo 10.5281/zenodo.22242109), screened with PARI ellrank (2-descent): 16 independent points, 2-Selmer upper bound 16.",
  "created_at": "2026-09-27 06:36:13",
  "updated_at": "2026-09-27 06:36:13"
}