{
  "id": 2962,
  "curve_key": "4310422130507421273655297312088372005561:-282683556238186420323291691971908859296368338659755630784941",
  "ainvs": [
    "1",
    "0",
    "1",
    "-89800461052237943201152027335174416783",
    "327180041942345393885215345805726536326256241541230408306"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 273.78556340460153,
  "faltings_height": 20.592474616574112,
  "conductor": "3812079870065732122018767404589934530",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "29",
    "31",
    "47",
    "67",
    "79",
    "199",
    "269",
    "617",
    "859",
    "2539",
    "5407",
    "85808363"
  ],
  "discriminant": "102155643642707638584323698967601795759877507474928171604550839943691225762114094199006106602570080227649278250000",
  "regulator": "497146176.446804164467731024618586934915942338391945133",
  "points": [
    [
      "9654599117446146915",
      "18976569002992092038027175892"
    ],
    [
      "5879280510277370115",
      "-1562304332719466085943530008"
    ],
    [
      "-10940884010435854149",
      "143024813315446773570559924"
    ],
    [
      "12634472754741182212995/2401",
      "69254096845812086166278866990408/117649"
    ],
    [
      "61105948739939193607707/11881",
      "1515350804145806700298991791813096/1295029"
    ],
    [
      "3350327435872072973596495500/373223761",
      "-112726671639541449979769632143354121537897/7210309838759"
    ],
    [
      "1055471153248644673858870345755/187443104809",
      "-20158777152426029225501083455844479744975784/81152929897742123"
    ],
    [
      "678008462173179290",
      "16328081542322324711249989017"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-032, rational kernel x=-44950628272970786809/4. 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 20:30:32",
  "updated_at": "2026-09-26 20:30:32"
}