# Stored data for abelian variety isogeny class 2.5.a_i, downloaded from the LMFDB on 08 January 2026.
{"abvar_count": 34, "abvar_counts": [34, 1156, 15538, 374544, 9759394, 241429444, 6103483378, 153413222400, 3814700709154, 95245771247236], "abvar_counts_str": "34 1156 15538 374544 9759394 241429444 6103483378 153413222400 3814700709154 95245771247236 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.397583617650433, 0.602416382349567], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 6, "curve_counts": [6, 42, 126, 598, 3126, 15450, 78126, 392734, 1953126, 9753162], "curve_counts_str": "6 42 126 598 3126 15450 78126 392734 1953126 9753162 ", "curves": ["y^2=x^6+3*x^5+x^4+2*x^2+3*x+3"], "dim1_distinct": 0, "dim1_factors": 0, "dim2_distinct": 1, "dim2_factors": 1, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "endomorphism_ring_count": 2, "g": 2, "galois_groups": ["4T2"], "geom_dim1_distinct": 1, "geom_dim1_factors": 2, "geom_dim2_distinct": 0, "geom_dim2_factors": 0, "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": 2, "geometric_extension_degree": 2, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.4.1"], "geometric_splitting_field": "2.0.4.1", "geometric_splitting_polynomials": [[1, 0, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 1, "is_cyclic": true, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 1, "label": "2.5.a_i", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 24, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["4.0.256.1"], "p": 5, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 2, 1, 2]], "poly": [1, 0, 8, 0, 25], "poly_str": "1 0 8 0 25 ", "primitive_models": [], "principal_polarization_count": 3, "q": 5, "real_poly": [1, 0, -2], "simple_distinct": ["2.5.a_i"], "simple_factors": ["2.5.a_iA"], "simple_multiplicities": [1], "singular_primes": ["3,2*F+V"], "size": 3, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.256.1", "splitting_polynomials": [[1, 0, 0, 0, 1]], "twist_count": 16, "twists": [["2.5.a_ai", "2.625.abc_cdq", 4], ["2.5.ai_ba", "2.390625.ddc_edrbq", 8], ["2.5.ag_s", "2.390625.ddc_edrbq", 8], ["2.5.ae_o", "2.390625.ddc_edrbq", 8], ["2.5.ac_c", "2.390625.ddc_edrbq", 8], ["2.5.a_ag", "2.390625.ddc_edrbq", 8], ["2.5.a_g", "2.390625.ddc_edrbq", 8], ["2.5.c_c", "2.390625.ddc_edrbq", 8], ["2.5.e_o", "2.390625.ddc_edrbq", 8], ["2.5.g_s", "2.390625.ddc_edrbq", 8], ["2.5.i_ba", "2.390625.ddc_edrbq", 8], ["2.5.ae_l", "2.59604644775390625.akvffce_bhpsebnknczgg", 24], ["2.5.ac_ab", "2.59604644775390625.akvffce_bhpsebnknczgg", 24], ["2.5.c_ab", "2.59604644775390625.akvffce_bhpsebnknczgg", 24], ["2.5.e_l", "2.59604644775390625.akvffce_bhpsebnknczgg", 24]], "weak_equivalence_count": 2, "zfv_index": 9, "zfv_index_factorization": [[3, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 2, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 324, "zfv_singular_count": 2, "zfv_singular_primes": ["3,2*F+V"]}