{
  "id": 2949,
  "curve_key": "118007714894514823001619459920892114967201:-56018565248553044398456274241391418404397364730190480543890801",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2458494060302392145867072081685252395150",
    "64836302371010468053563961422511164548489508727209655522500"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 284.36157747546423,
  "faltings_height": 21.717995426459762,
  "conductor": "5360073200986915269158012602792104734070",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "23",
    "29",
    "47",
    "61",
    "97",
    "101",
    "109",
    "151",
    "727",
    "1063",
    "2707",
    "3571",
    "7681",
    "131143"
  ],
  "discriminant": "-865003104665697317366768650959123545956852676938822778320321891616784106042102267405522106528362109727799507249539000000",
  "regulator": "2578359876.10585668404104538730823983323782097398111220",
  "points": [
    [
      "43155499697406724159576/625",
      "7399831333312344070346106716218726/15625"
    ],
    [
      "-22883762348251578050",
      "-330321713827001137778136788900"
    ],
    [
      "-548648125152481694",
      "-257264426955158632651117708328"
    ],
    [
      "154591304487277414540709200/1079521",
      "-1825692024376487379987807495255690705950/1121622319"
    ],
    [
      "-1080163835584214166092666/54289",
      "4115903623771839840402016120509527894/12649337"
    ],
    [
      "-159705102986780530265696570/2699449",
      "-251261318335932108099008095921699664500/4435194707"
    ],
    [
      "-21988967777062815197600/961",
      "9840517216384251577948579839279250/29791"
    ],
    [
      "425159882099985247297390/326041",
      "-46218267119142302327661259147365437390/186169411"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-039, rational kernel x=29778866334177098428. 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 20:29:43",
  "updated_at": "2026-09-26 20:29:43"
}