{
  "id": 2950,
  "curve_key": "134580151493486229621831994191622958629733929:-1561246648930120417924048384299321974878528109557122724153438071637",
  "ainvs": [
    "1",
    "0",
    "1",
    "-2803753156114296450454833212325478304786124",
    "1806998436261713446671118650546390909182980742553050103837376702"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 304.8322015475566,
  "faltings_height": 22.789456468881163,
  "conductor": "122397238576536479651595594069449949746370",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "31",
    "37",
    "41",
    "53",
    "59",
    "107",
    "109",
    "149",
    "179",
    "241",
    "419",
    "1789",
    "1879",
    "1405127849"
  ],
  "discriminant": "332280796251037410218221268922713396876335331802926593035799574817180361624915425115218891019736585154207389016544730940",
  "regulator": "5793943444.10745291605994667597061995254227260041038396",
  "points": [
    [
      "422303415191139388280",
      "26424942153581441228336420182026"
    ],
    [
      "966730155477531374903",
      "128326003979081279509471317"
    ],
    [
      "24168822175414805367281/25",
      "-73173840472162383415832948019/125"
    ],
    [
      "323751282648029395262594150542696005437/3453859772124304",
      "5824362814581067129234143517452918623414264685585464213343/202981777663128345894592"
    ],
    [
      "3097294272082479180613363501629293/3203827925776",
      "-814187311942100790828035073652013706673966959/5734608496216681024"
    ],
    [
      "5073919521485627528927029028575519/5248264046281",
      "-26284477715473528121284575947163579312760349095/12023295338001559429"
    ],
    [
      "2224773435614129883042732887/2316484",
      "1200469823681049505302119999944437397857/3525688648"
    ],
    [
      "170833481105072405391835981446659/176718503641",
      "159279728765219403813905249363839945163204745/74288747842099939"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-062, rational kernel x=-483365240359059394959. 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 20:29:46",
  "updated_at": "2026-09-26 20:29:46"
}