{
  "id": 273,
  "curve_key": "9684913692500090356012555202915243565710817455750531285486666641:-994557259417874600793726224085029793887754159405457725835627998281306921883628926505055206421689",
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  "rank_lower_bound": 30,
  "naive_height": 442.08542264233836,
  "faltings_height": 34.77051188023562,
  "conductor": "2381958488309327728488641214562148525681586925734398576894288277390640894675828305511266759053188773997283310012808983216600083938367948090232306090",
  "bad_primes": [
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    "31",
    "41",
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    "67",
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  "discriminant": "-46714661255308767314567688733841531918983356002159772613256840842851650254036518701100578342601553513579222272710220496887616034526983492843954090554197033638137245037791044053017600000000",
  "regulator": "10720686604115654188358042985326663938.588084900092986474567459949780498792191278825612795832355129",
  "points": [
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      "30786757706172245427369935940751/4",
      "58841476683002984849182029306774218124047405249/8"
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    [
      "245309280348041323814668746104926/25",
      "1346501028820415725958868015485008289981037919061/125"
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    [
      "20286216384652039303944170492166526/9409",
      "-24593234902246769413006506020777691495865223432164871/912673"
    ],
    [
      "-25558163204018019740775243468600589874/1760929",
      "74707049582033426178338768659390679551818201954095350999/2336752783"
    ],
    [
      "4546264873863829383537112534021848799606/398521369",
      "-145386763829319577901520209264368135012688669041886277075149/7955682089347"
    ],
    [
      "1709164065046406773620054102684586/169",
      "26450264171408287955631955124255640794301463854841/2197"
    ]
  ],
  "submitter": "ranksunbounded",
  "commentary": "Note: the original submission silently dropped one of the witness points, possibly due to the parser bug fixed in https://github.com/icarm/elliptic-rank/commit/7717d4da140cd7ba4ef702c6f7841e00f3194c38.\r\n\r\nUnder GRH+BSD the rank is exactly 30 (if one applies https://arxiv.org/abs/1112.1503 with Delta=4.25 one gets an upper bound of 31 on the analytic rank, and the root number is 1, so the rank is even).",
  "created_at": "2026-08-20 08:10:53",
  "updated_at": "2026-08-20 11:24:48"
}