{
  "id": 3020,
  "curve_key": "29574350406255936977855844569761:-160361129890704980435639249356741141807659600241",
  "ainvs": [
    "1",
    "0",
    "0",
    "-616132300130332020371996761870",
    "185603159595723305641335231450041290536912900"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 217.39338070547726,
  "faltings_height": 15.930372027189858,
  "conductor": "40671677445041477433310596010",
  "bad_primes": [
    "2",
    "5",
    "7",
    "19",
    "23",
    "29",
    "37",
    "53",
    "107",
    "131",
    "239",
    "263",
    "3329",
    "7971031"
  ],
  "discriminant": "87548021298889308131282306442204280873299720619317731961309524235585237521489332736000000",
  "regulator": "5674590.34844152186113424041288787060845033807271773148",
  "points": [
    [
      "16434083313668849140/32041",
      "12189501720225897921101387670/5735339"
    ],
    [
      "-711811809841060",
      "16233158065603405428130"
    ],
    [
      "11934929964754396/25",
      "64469800012437988787866/125"
    ],
    [
      "13519518900407255164/27889",
      "4273365559662189105238209486/4657463"
    ],
    [
      "8514695157228947100/29929",
      "29897598545591089995784966410/5177717"
    ],
    [
      "11364772098318535895826/28462225",
      "273620377318647192192557447347146/151845970375"
    ],
    [
      "-11546736210416251590/12769",
      "2625721021789947157763356710/1442897"
    ],
    [
      "91732129715656398740/212521",
      "27029038689789145006046935530/97972181"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-066, rational kernel x=-236532652199492. 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 20:33:36",
  "updated_at": "2026-09-26 20:33:36"
}