{
  "id": 3239,
  "curve_key": "497464619249885254753018957237122106764467425:-8996515035422379050165990984630966639980445699002803879744115260625",
  "ainvs": [
    "1",
    "0",
    "0",
    "-10363846234372609474021228275773377224259738",
    "10412633142849975752506070356136680338076754827045078931231445092"
  ],
  "rank_lower_bound": 18,
  "torsion": [
    2
  ],
  "naive_height": 308.7542950282019,
  "faltings_height": 23.73538083626648,
  "conductor": "235186508255669484903975893032399896944786213691049874204261617969438950",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "31",
    "37",
    "47",
    "71",
    "73",
    "79",
    "137",
    "149",
    "163",
    "307",
    "601",
    "1063",
    "1187",
    "1229",
    "3313",
    "5261",
    "7229",
    "7879",
    "15131",
    "59999",
    "363833"
  ],
  "discriminant": "24404402540702114714152735230783157665020598266113141250940854330021962187436300392679766515254504089525626949949060592697344000000",
  "regulator": "51607178400795077394.065527005299917055763583465357002051022220996867655661",
  "points": [
    [
      "-2607430220370914397748",
      "-140387047515681414866483277225226"
    ],
    [
      "-1605621491785584326188",
      "-151372793043869629484835629808106"
    ],
    [
      "-2819922555961640428588",
      "-131201968173035899303243763491306"
    ],
    [
      "875074463835213331412",
      "44873030649530301538628591068694"
    ],
    [
      "-2467740801703347504172",
      "-144775716117584701878214589749738"
    ],
    [
      "13315637656440444494452",
      "1494441905162102144306674307907574"
    ],
    [
      "-1762195702769915024758",
      "-152327124138187809062915466865846"
    ],
    [
      "-3041170932937489746148",
      "-117490087567011259916929625833426"
    ],
    [
      "193937709055224344613248/169",
      "12175020573097089290719700040789038/2197"
    ],
    [
      "1137909325716961985492",
      "9639692990949146169233800248854"
    ],
    [
      "3675715656247791166436",
      "148257394272207471703227166795334"
    ],
    [
      "52674857918538925070492",
      "12067240814424463070666174122025654"
    ],
    [
      "24178122670442307993524/25",
      "4496666863426713185668843068346558/125"
    ],
    [
      "3043510109618488310996",
      "84036038998028036136847099902230"
    ],
    [
      "1003524686553582969812",
      "31982322815500336822454512655894"
    ],
    [
      "673212038823402740957972/1681",
      "5481850155437583218016483153847046374/68921"
    ],
    [
      "644529864811619733766772/841",
      "1317924596196559752853144019460116206/24389"
    ],
    [
      "22583923428257353747412",
      "3360790983252352570792019048207894"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Voznyy (2024). Source: https://dujella.github.io/tors/z2old141516171819.html (curve entry 10). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:44:09",
  "updated_at": "2026-09-26 20:44:09"
}