{
  "id": 3207,
  "curve_key": "9339418986312525794535587159829601:-183058132719507247700746477026134876165988315895825",
  "ainvs": [
    "1",
    "0",
    "0",
    "-194571228881510954052824732496450",
    "211872838795725964920854163839521046715980990916"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 234.6586563362292,
  "faltings_height": 17.620580937985835,
  "conductor": "25369082817839617747015394004038159673868651735600634772174",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "37",
    "41",
    "47",
    "79",
    "83",
    "101",
    "373",
    "433",
    "467",
    "733",
    "911",
    "1289",
    "1447",
    "1949",
    "2011",
    "29629",
    "31751"
  ],
  "discriminant": "452035982795747070511150179730472582897708589488717563990299065699756677159326623335737310839508992",
  "regulator": "85805842332195324.813846195694815110583521957094484789307042872401395",
  "points": [
    [
      "1715833272333801972/49",
      "2067584443541015776493800242/343"
    ],
    [
      "-1031700937567825836/169",
      "-2378620581721364526927287178/2197"
    ],
    [
      "115018223996543973716/3721",
      "1105737108029117551254116038358/226981"
    ],
    [
      "3179983030768454184/25",
      "-5636800471249830277418106558/125"
    ],
    [
      "-2181504880021970296/169",
      "-1662502590368954947229469754/2197"
    ],
    [
      "-49221084312011976443414456373288364/4127848608236356081",
      "-7670547989487975717615849341287163321651021367432878/8386594428876980664722775479"
    ],
    [
      "-40998541119059968169388/3052009",
      "-3378570069922954332575650140627078/5331859723"
    ],
    [
      "44497527978517621957716/546121",
      "9249796507862907899593747385794842/403583419"
    ],
    [
      "77935390874667434881191794121604553585237455106/5828390615467915081650070369609",
      "-447271397282264050538052415872007108822572545319125572080204984233372/14070935600280373192348131085328641339476910523"
    ],
    [
      "55948543399703789069213316/84732025",
      "-418394925943226853198854430218221734954/779958290125"
    ],
    [
      "-38240381897144887089637394506848/5980720321403689",
      "-505513032792128962177429667000739295440849917466/462519705800031893046613"
    ],
    [
      "437107598646611797882986852272525/400638356536320016",
      "-7560617303188050636965009490595425111095192284369/253588052550675691182079936"
    ],
    [
      "3688971648692701958886/156025",
      "-183120080409493765504194784399194/61629875"
    ],
    [
      "167792993899535990579355320966437446905656065366/7015886561567206891834162393225",
      "-56482635005461170001094374353536438594106377683956269328094213547622456/18583342772479926359172729446179801865222070875"
    ],
    [
      "-69632802922580518213304286/5073285529",
      "-196852012206461973428376604850373988122/361354908374083"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2old141516171819-043, rational kernel x=115715265331868383/4. Source: https://dujella.github.io/tors/z2old141516171819.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.",
  "created_at": "2026-09-26 20:42:41",
  "updated_at": "2026-09-26 20:42:41"
}