# Stored data for abelian variety isogeny class 4.5.ae_m_abk_ec, downloaded from the LMFDB on 24 August 2026.
{"abvar_count": 324, "abvar_counts": [324, 571536, 195608196, 171634546944, 109520787787524, 60000896380246416, 37198818832478567364, 23397299474082655371264, 14510470979068811530817796, 9073965668183699904215730576], "abvar_counts_str": "324 571536 195608196 171634546944 109520787787524 60000896380246416 37198818832478567364 23397299474082655371264 14510470979068811530817796 9073965668183699904215730576 ", "angle_corank": 2, "angle_rank": 2, "angles": [0.196618866692638, 0.196618866692638, 0.619957764542144, 0.619957764542144], "center_dim": 4, "curve_count": 2, "curve_counts": [2, 34, 98, 698, 3562, 15730, 78010, 392538, 1947554, 9743074], "curve_counts_str": "2 34 98 698 3562 15730 78010 392538 1947554 9743074 ", "curves": ["y^2=2*x^10+x^9+3*x^8+x^7+2*x^6+x^4+x^3+4*x^2+3", "y^2=2*x^10+x^9+2*x^7+4*x^6+3*x^4+x^3+3*x^2+x+1", "y^2=2*x^10+x^9+2*x^8+4*x^6+4*x^5+3*x^3+2"], "dim1_distinct": 0, "dim1_factors": 0, "dim2_distinct": 1, "dim2_factors": 2, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "g": 4, "galois_groups": ["4T3"], "geom_dim1_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_distinct": 1, "geom_dim2_factors": 2, "geom_dim3_distinct": 0, "geom_dim3_factors": 0, "geom_dim4_distinct": 0, "geom_dim4_factors": 0, "geom_dim5_distinct": 0, "geom_dim5_factors": 0, "geometric_center_dim": 4, "geometric_extension_degree": 1, "geometric_galois_groups": ["4T3"], "geometric_number_fields": ["4.0.90944.1"], "geometric_splitting_field": "4.0.90944.1", "geometric_splitting_polynomials": [[18, 4, 4, -2, 1]], "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 3, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": false, "is_supersingular": false, "label": "4.5.ae_m_abk_ec", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 6, "newton_coelevation": 6, "newton_elevation": 0, "noncyclic_primes": [2, 3], "number_fields": ["4.0.90944.1"], "p": 5, "p_rank": 4, "p_rank_deficit": 0, "poly": [1, -4, 12, -36, 106, -180, 300, -500, 625], "poly_str": "1 -4 12 -36 106 -180 300 -500 625 ", "primitive_models": [], "q": 5, "real_poly": [1, -4, -8, 24, 36], "simple_distinct": ["2.5.ac_e"], "simple_factors": ["2.5.ac_eA", "2.5.ac_eB"], "simple_multiplicities": [2], "slopes": ["0A", "0B", "0C", "0D", "1A", "1B", "1C", "1D"], "splitting_field": "4.0.90944.1", "splitting_polynomials": [[18, 4, 4, -2, 1]], "twist_count": 6, "twists": [["4.5.a_e_a_ba", "4.25.i_cq_ps_eaw", 2], ["4.5.e_m_bk_ec", "4.25.i_cq_ps_eaw", 2], ["4.5.c_a_am_abd", "4.125.abc_rc_akie_flly", 3], ["4.5.a_ae_a_ba", "4.625.cu_fgm_hemy_iatsg", 4], ["4.5.ac_a_m_abd", "4.15625.ea_adaq_dakqa_bwrtmqo", 6]]}