{
  "id": 2986,
  "curve_key": "33079603711287877052849543531809106896:-190237712529728944326888215097066084599300058590861909056",
  "ainvs": [
    "0",
    "1",
    "0",
    "-689158410651830771934365490246023060",
    "220182537650149240889364112070994007271068052546304708"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 259.1759407144867,
  "faltings_height": 19.293922091964678,
  "conductor": "6529827304278763417963592037876180",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "19",
    "23",
    "29",
    "37",
    "43",
    "97",
    "101",
    "227",
    "797",
    "4507",
    "16657",
    "216919"
  ],
  "discriminant": "4227950808344993376606787623346355276101505737338850634872564481872972544516179407317849745117187500000000",
  "regulator": "83020859.1341720221566636681853789524173045860873064686",
  "points": [
    [
      "456646453318362212425259224/134629609",
      "-9489780032728690978471705245008224218750/1562107353227"
    ],
    [
      "27785968405176244022957464/1940449",
      "-146225655570674369207536724214206156250/2703045457"
    ],
    [
      "66173212753899203166133936/136866601",
      "2851001296114495398675149781143140950/1601202365099"
    ],
    [
      "-859601160947373764",
      "421203562745187898324406250"
    ],
    [
      "763898559084675769591/1681",
      "2010574560782564798715655335000/68921"
    ],
    [
      "23241330272769834982131/15625",
      "-3079539463892589748107292098587154/1953125"
    ],
    [
      "486175045421626236",
      "-6800868607330534981406250"
    ],
    [
      "40614914756965860235286928935252634177784/123848975805155571794209",
      "7479455646409100549798858028203329109940308022475455374155590/43585158450853122007983246396560177"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-075, rational kernel x=-241608309854211556. Source: https://dujella.github.io/tors/z6old678.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 20:32:00",
  "updated_at": "2026-09-26 20:32:00"
}