{
  "chi8_is_the_character_of_Q_sqrt2": true,
  "chi8_even": true,
  "chi8_matches_attack09": true,
  "conductor": 8,
  "discriminant_of_K": 8,
  "signature": [
    2,
    0
  ],
  "unit_rank": 1,
  "unit_rank_expected": 1,
  "epsilon_inverse_is_sqrt2_minus_1": true,
  "sigma_acts_by": -1,
  "sigma_is_minus_inverse": true,
  "chi8_eigenspace_dimension": 1,
  "chi8_eigenspace_dimension_claimed": 1,
  "plus_eigenspace_dimension": 0,
  "trivial_eigenspace": "the units of Q, rank 0",
  "eleven_inert_in_K": true,
  "local_field_at_11": "Q₁₁(√2), unramified quadratic",
  "kummer": {
    "epsilon": "1 + √2",
    "epsilon_24_mod_121": [
      1,
      110
    ],
    "epsilon_24_minus_1_in_11O": true,
    "log_epsilon_mod_121": [
      0,
      55
    ],
    "log_over_11_sqrt2_mod_11": 5,
    "norm": -1,
    "sigma_epsilon": "1 − √2 = −ε⁻¹",
    "nonzero": true
  },
  "cited": "Soulé / Bloch–Kato: H¹_f(Q, Q₁₁(χ)(1)) is the χ-part of the global units ⊗ Q₁₁ — CITED_THEOREM",
  "conclusion": "H¹_f(Q, Q₁₁(χ₈)(1)) is a ONE-DIMENSIONAL Q₁₁-line spanned by the Kummer class κ(ε); any nonzero class in it is a scalar multiple of κ(ε)",
  "target_is_a_line": true,
  "agrees": true
}