{
  "id": 2160,
  "curve_key": "660618095050242273807609090346532878830081:-536670577987533927583551888563170399562380243581765435076914945",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-13762876980213380704325189382219434975627",
    "621146502300386490262181331007982048373280653342968556749595"
  ],
  "rank_lower_bound": 17,
  "torsion": [
    2
  ],
  "naive_height": 288.8819835935713,
  "faltings_height": 21.822335692832066,
  "conductor": "18331238590268621233314106535710120397922860155863660882325091066952394194",
  "bad_primes": [
    "2",
    "3",
    "43",
    "59",
    "71",
    "83",
    "151",
    "157",
    "163",
    "233",
    "331",
    "503",
    "617",
    "1061",
    "1097",
    "9109",
    "43607",
    "45589",
    "53831",
    "290761",
    "6923687",
    "322437920267"
  ],
  "discriminant": "167346072033141183429379974632006750478031033425544727192802267569739842854291376330645576230692810897297755053609923072",
  "regulator": "291306530825459573589.263553812254122806167708695568174099517048569457533",
  "points": [
    [
      "35360257945300555995",
      "-422729516876384594460951251670"
    ],
    [
      "1795477355583361323419/25",
      "7016454011674617921658865466018/125"
    ],
    [
      "8042534823227187151463/121",
      "-4470343076563974693107801183826/1331"
    ],
    [
      "-222236952471336952523477821/1651225",
      "399786565617662902933241130471909987138/2121824125"
    ],
    [
      "3076918214978948628065/49",
      "-23065552301012127312354975831750/343"
    ],
    [
      "169616357746587882696013796381/2151568225",
      "16123424571895817878306388995737308200342716/99800492116625"
    ],
    [
      "6350120824115880105215/121",
      "277304117566453918626908244761514/1331"
    ],
    [
      "34051983603060618910385/289",
      "3916009758964012636407174268554870/4913"
    ],
    [
      "1651450848225731941906901649/2512225",
      "66108899232990349485868492316969219860662/3981876625"
    ],
    [
      "585876868897391207539019/3025",
      "-380147686893069543468360556399554282/166375"
    ],
    [
      "443443160018110195141043/6889",
      "25232260468558752555555842967341070/571787"
    ],
    [
      "104985009666244650384291029/1585081",
      "-23725863743404280556855679074238879950/1995616979"
    ],
    [
      "442195557691070119166753189667/217474009",
      "293571304396435706625853871949608518202109742/3207089210723"
    ],
    [
      "6290714661454804173401991011/87403801",
      "-47781477300792823777384499957558203111806/817138135549"
    ],
    [
      "352717977739600905389025729791/5061326449",
      "-7837980165796659907752507783234179288319210/360077947561207"
    ],
    [
      "2219104709823743305531313609628741275/44857193611738561",
      "-2353396242240633041825819901056218117061080779680486214/9500536901863888910811809"
    ],
    [
      "175282208143880501962582013156075/2476660735081",
      "-155720487632259008366774888759560572060772310166/3897622541887108021"
    ]
  ],
  "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=74/4903 (the 2-isogenous partner of that fibre). Found by a Mestre-Nagao sieve over t=a/b with |a|,b<=30000, screened with PARI ellrank (2-descent): 17 independent points, 2-Selmer upper bound 17.",
  "created_at": "2026-09-26 14:17:18",
  "updated_at": "2026-09-26 14:17:18"
}