{
  "id": 3472,
  "curve_key": "43392756672011539792095213444394190411521:-6207381397313562622826565761141615252314969881672411133723265",
  "ainvs": [
    "1",
    "1",
    "1",
    "-904015764000240412335316946758212300240",
    "7184469209853660442709629729284176740595203450045665168561"
  ],
  "rank_lower_bound": 17,
  "torsion": [
    2
  ],
  "naive_height": 280.7133334709611,
  "faltings_height": 21.423223495697084,
  "conductor": "199500119263603519815431870142834901369753749343131572760786463422",
  "bad_primes": [
    "2",
    "3",
    "7",
    "17",
    "19",
    "29",
    "31",
    "37",
    "43",
    "47",
    "59",
    "61",
    "83",
    "163",
    "193",
    "263",
    "653",
    "701",
    "947",
    "1693",
    "2311",
    "4637",
    "10457",
    "56599",
    "57329",
    "7057319"
  ],
  "discriminant": "24984952135622030580355191580126836742053515039282183032224538975281620665697360898253951150220631192853146758374490112",
  "regulator": "4512021069038085583348.61363632664949565605382890397516686488745090805396",
  "points": [
    [
      "-33424291830823600843",
      "7713352039302469893427633029"
    ],
    [
      "-22853316985022103359",
      "126129031273944385546553825237"
    ],
    [
      "-1292182814575415548842815/53824",
      "1531937636804193991090743695207993891/12487168"
    ],
    [
      "1161374041361208983051/25",
      "31976848787465082227223855165261/125"
    ],
    [
      "10548217603692010968261/169",
      "967457328321304210825416859656897/2197"
    ],
    [
      "11294050591060626731461/1369",
      "859545321481079463596302179207953/50653"
    ],
    [
      "2292186329875052117813293/22801",
      "3324347939567895002490140558737502219/3442951"
    ],
    [
      "6701930286236795218061013/1324801",
      "79827971691653499892626815283279672027/1524845951"
    ],
    [
      "10390451257052292064199101/81225",
      "32613606100305868570510369796403735769/23149125"
    ],
    [
      "251615090981840726613336613/237169",
      "3989622958614706494341266247571836039507/115501303"
    ],
    [
      "1162264485227951336938512597/5067001",
      "39293936457519141858606800904198788613159/11405819251"
    ],
    [
      "3804631167919789487641954093/1734489",
      "234654121795686378269890761356004949341649/2284322013"
    ],
    [
      "20079620248390600710896602285/13951625689",
      "126433081074179344781981973384163475234895761/1647924171507613"
    ],
    [
      "63381628989597542002095484077/7315551961",
      "982967124103581758585166267556160304159983/625706474776291"
    ],
    [
      "2463245100130886757513078631965/66951045001",
      "2668418806611354722336053921738843452116361273/17323515942963749"
    ],
    [
      "9343372809145410733570889197021/50014402321",
      "28203435734267064111243142558502207136850797923/11185170920666119"
    ],
    [
      "56292945441871788928842770203229/2264004724921",
      "30223171086319218389687054160711971586291635169/3406559613404356781"
    ]
  ],
  "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=1546/487. 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): 17 independent points, 2-Selmer upper bound 17.",
  "created_at": "2026-09-27 06:36:16",
  "updated_at": "2026-09-27 06:36:16"
}