{
  "id": 38,
  "curve_key": "1256446084449882436622961685809657787370709070536721:-44123945595377604327137242899392065760392800145803979335441014758961586480505",
  "ainvs": [
    "1",
    "0",
    "0",
    "-26175960092705884096311701787701203903556438969515",
    "51069381476131486489742177100373772089779103253890567848326775119094885041"
  ],
  "rank_lower_bound": 18,
  "naive_height": 352.9803807313966,
  "faltings_height": 27.276890974701136,
  "conductor": "25725142933318819706009609339333397294766021498979988120833604560475705134314952598",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "29",
    "31",
    "41",
    "47",
    "53",
    "79",
    "107",
    "109",
    "137",
    "149",
    "181",
    "313",
    "487",
    "2063",
    "3209",
    "3329",
    "6469",
    "10513",
    "15091",
    "18913",
    "23417",
    "32441",
    "47051",
    "131749",
    "643889"
  ],
  "discriminant": "21165818183141855603806249764561281249470640134499286938938173449471997510627809748094469486747147781730447578406918725587571677363134437997346291712",
  "regulator": "90710216574493228744.822722175775048901778182334992644131077527874357834918",
  "points": [
    [
      "3231737970618117409726910",
      "477734049899522560689163862493530849"
    ],
    [
      "3273309887687276930053886",
      "677805198733135867174443509568209441"
    ],
    [
      "3241000828313547371069168",
      "526142335107247006178138422111656119"
    ],
    [
      "3255153282123996886918526",
      "595229162470140060497670577715082401"
    ],
    [
      "26966585148660027255767774",
      "137677903994541133602151567271381542145"
    ],
    [
      "4770216163266413128311686",
      "5894953964627833789313924429835166673"
    ],
    [
      "2549750315144935427762366",
      "950643850306503428886497351231138273"
    ],
    [
      "3713349702880881629511998",
      "2252141359101383750330981276127632993"
    ],
    [
      "3542121340287734605297214",
      "1671112741117758577475984222816297825"
    ],
    [
      "3195043262517282313487906",
      "228081804454697230002446209771949321"
    ],
    [
      "5646805757967450691937630",
      "9127716726638497548695728027642334081"
    ],
    [
      "14331333023247963581855678",
      "51180113307318927046718773937933570273"
    ],
    [
      "97191985119716082916503194/25",
      "354969759255330273188266145971062270037/125"
    ],
    [
      "1185147271535670890597935886/169",
      "32017173765694036331237894920457649821237/2197"
    ],
    [
      "98739463791232711776641098401842/38278969",
      "199867994868228186007608230146203388221790785839/236831981203"
    ],
    [
      "2294824481268463496752138910",
      "109931747845168723937902307597670194926241"
    ],
    [
      "-52959420769695630752203586/9",
      "31331086291021542344530429579191837787/27"
    ],
    [
      "154432285705268244684426598052/44521",
      "13312631160178214785941322691372196088408619/9393931"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Found by Elkies (2006). A curve of rank exactly 18, via Dujella's elliptic-curve rank-records tables.",
  "created_at": "2026-05-27 22:12:16",
  "updated_at": "2026-07-01 22:33:41"
}