{
  "id": 2730,
  "curve_key": "458322304200445226084651160802453307579916123121:-326301547980907055375132683690278239666819437055174483157896473932702025",
  "ainvs": [
    "1",
    "0",
    "0",
    "-9548381337509275543430232516717777241248252565",
    "377663828681605388165662032646784651619190173701890369766128592660321"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    10
  ],
  "naive_height": 329.33238672843834,
  "faltings_height": 25.382270643658178,
  "conductor": "763384827925528186459799976258",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "17",
    "23",
    "37",
    "41",
    "59",
    "79",
    "101",
    "131",
    "439",
    "1901",
    "4163681"
  ],
  "discriminant": "-5901517358351803348368744952578871502995381497346613443643396550315951162795247782767649156689773294385517057042862890306464137726119641088",
  "regulator": "1498194.032403684042537374664115676953141968527",
  "points": [
    [
      "9533146388344013080424422882/227529",
      "776228258355276017285491239695684479112659/108531333"
    ],
    [
      "27510916627425275007607725344914/396209025",
      "-55450345866065844698197155751876257600336498697/7886540642625"
    ],
    [
      "45428941003353162664779475629185959471389196637315618362584526971842/8459767238371502648537753352041554715218009",
      "306145257621983760049880172345317285114975391963653917190468176883288869531968564145904431681551097093/24605807444758116078074103437873769134330331519840918006158981027"
    ],
    [
      "-100118220993960898126186180741820232840981729205246/931625709524483383444725625",
      "-362671469095748395211471276382255202583678771423801204872226165676600812683/28435586974398536014008539902294651421875"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z10-018, rational kernel x=907799169750913420899183/4. 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 20:19:43",
  "updated_at": "2026-09-26 20:19:43"
}