{
  "control_A": {
    "matrix": [
      [
        3,
        1
      ],
      [
        7,
        2
      ]
    ],
    "det": -1,
    "det_mod_11": 10,
    "accepted_for_char0_nonvanishing": true
  },
  "control_B": {
    "B": [
      [
        1,
        2
      ],
      [
        1,
        4
      ]
    ],
    "U": [
      [
        2,
        1
      ],
      [
        1,
        1
      ]
    ],
    "V": [
      [
        1,
        3
      ],
      [
        0,
        1
      ]
    ],
    "B_prime": [
      [
        3,
        17
      ],
      [
        2,
        12
      ]
    ],
    "det_B": 2,
    "det_B_prime": 2,
    "same_determinant_line": true,
    "accepted": true
  },
  "B_N": {
    "integral_lattice": "E(Q) (x) Z_11 is free of rank 2 (Sha[11^inf] = 0, torsion trivial)",
    "integral_target": "(+)_l E(F_l) (x) Z_11 = (+)_l Z/11 - TORSION: loc over Z_11 has no characteristic-zero determinant",
    "so": "B_N has no integral lift; a mod-11 nonvanishing of det(loc_n) is a statement about E(Q)/11 only",
    "char0_source_that_exists": "the Z_11-adic Kolyvagin system {kappa_n} (Kim section 2.5), non-trivial <=> IMC_11 (Kim); IMC_11 here: CLOSED (Burungale-Castella-Skinner), cited, external - not checked by this line (RUN-021)",
    "char0_element_that_would_be_canonical": "BKS's eta^BSD / N(z_F) leading term - conjectural (GPR)"
  },
  "char0_verdict": "UNMEASURED",
  "agrees": true
}