{
  "id": 2942,
  "curve_key": "4979884642282703979942392812854056308351681:-11853166152343167678513483798404797772818818136782036087956965921",
  "ainvs": [
    "1",
    "0",
    "0",
    "-103747596714222999582133183601126173090660",
    "13718942305952740368641219874353441801908454337456892365155600"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 295.07091175273996,
  "faltings_height": 22.538772025769045,
  "conductor": "1375141440105163911081601881101260056990",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "23",
    "29",
    "31",
    "37",
    "47",
    "149",
    "167",
    "479",
    "617",
    "971",
    "1907",
    "6961",
    "8693281"
  ],
  "discriminant": "-9838043049096501137873029601269735247320109492134608494393362667226572721436819368338083293939323960488245232761358007808000",
  "regulator": "1720782250.72519802643238750040741716831593094339942573",
  "points": [
    [
      "285898651814442710487790/1681",
      "68698340814513357553246877515994090/68921"
    ],
    [
      "125651799867903472880",
      "1633005743562188872273976648540"
    ],
    [
      "534479031744001153880",
      "10533351570788889740799869048540"
    ],
    [
      "1793463313477957283543090/6889",
      "1193112916119856748446548010943681650/571787"
    ],
    [
      "605802921015861448079150/24649",
      "12941864429035178235877747568015633330/3869893"
    ],
    [
      "420840751832344849543246205424106756/2751655121600841",
      "-172554003246127863444385971012923312543620342065945988/144341429174475589281861"
    ],
    [
      "154824810006709362065264977211000/2604314936521",
      "-11708685421456822007543023014921406441318012129460/4202814797093288069"
    ],
    [
      "61322632269881729727223640/100489",
      "424591947367851956903165194659395837500/31855013"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-081, rational kernel x=187326769206971886920. 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 20:29:24",
  "updated_at": "2026-09-26 20:29:24"
}