{
  "id": 2726,
  "curve_key": "85804880709701490710592002376515989996425383413681:-794734244457887566612657174258565890470236196366278631135756968682973906921",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1787601681452114389804000049510749791592195487785",
    "919831301455888387283167876795422252219907558423929474955754599589003225"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    10
  ],
  "naive_height": 344.9284810599561,
  "faltings_height": 26.44152287665753,
  "conductor": "4528475143582181274801482317230",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "29",
    "41",
    "101",
    "113",
    "157",
    "239",
    "521",
    "36979",
    "618679"
  ],
  "discriminant": "77539873250657166354785047006922667669580127524950792443083747499723053879460361556469655943658200981030689606649614044565103284602880000000000",
  "regulator": "12902220.62075227260129714779280916488850934968",
  "points": [
    [
      "7189397741544483261909432783684507303183499124329633841843331544330/7040557219527856329385297437463037163509449",
      "7454119555772028929051798437552467417011916829642154678089412961873681479239081386340591541125336655/18681448568883872952806848466259839790198346286952842372892845957"
    ],
    [
      "14009386179844710063020841062599413350170137669830241980963417256170/17868469872397268895644371860440663555503129",
      "-1178601056247288989115774724437027037516271750325730992041363918819515231519319401178174457268762295/75532010762968692773989001281939245233768140146652103480837396867"
    ],
    [
      "70755424644626627378597549013825658193099790774526892885222805691024970/90865975315651813029485527397482707099739089841",
      "-79399238715994721822653616788404404357323347223836363153085028528392602239760547009496339342688010404565/27390624785745140865946740790207367254541518722385580140521978231270889"
    ],
    [
      "-58979920822806427940167983323678174005/108932931164836",
      "1494973251030490115916446594590896230344519390751593944485/1136943242262922826584"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z10-022, rational kernel x=-382712265091480194077830. Source: https://dujella.github.io/tors/z10.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 20:19:33",
  "updated_at": "2026-09-26 20:19:33"
}