# Stored data for abelian variety isogeny class 2.61.au_ih, downloaded from the LMFDB on 17 January 2026.
{"abvar_count": 2697, "abvar_counts": [2697, 13962369, 51802562772, 191829671847081, 713360732182135377, 2654345051475277346064, 9876832860651710126385417, 36751696027451928996398735625, 136753053222686025017780935878132, 508858108641936489298964389853893329], "abvar_counts_str": "2697 13962369 51802562772 191829671847081 713360732182135377 2654345051475277346064 9876832860651710126385417 36751696027451928996398735625 136753053222686025017780935878132 508858108641936489298964389853893329 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.199705063639539, 0.343962623824078], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 42, "curve_counts": [42, 3752, 228222, 13854676, 844617402, 51520298222, 3142742940162, 191707324320868, 11694146125511862, 713342910292233752], "curve_counts_str": "42 3752 228222 13854676 844617402 51520298222 3142742940162 191707324320868 11694146125511862 713342910292233752 ", "curves": ["y^2=23*x^6+25*x^5+24*x^4+5*x^3+47*x^2+59*x+30", "y^2=31*x^6+57*x^5+27*x^4+54*x^3+36*x^2+45*x+56", "y^2=24*x^6+36*x^5+12*x^4+5*x^3+8*x^2+3*x+54", "y^2=13*x^6+49*x^5+48*x^4+54*x^3+21*x^2+22*x+41", "y^2=35*x^6+19*x^5+40*x^4+23*x^3+36*x^2+2*x+42", "y^2=21*x^6+24*x^5+60*x^4+13*x^3+53*x^2+50*x+4", "y^2=53*x^6+9*x^5+54*x^4+40*x^3+16*x^2+52*x+9", "y^2=10*x^6+45*x^5+20*x^4+22*x^3+41*x^2+17*x+30", "y^2=7*x^6+32*x^5+48*x^4+51*x^3+9*x^2+13*x+30", "y^2=7*x^6+9*x^5+19*x^4+50*x^3+52*x^2+13*x+26", "y^2=40*x^6+60*x^5+21*x^4+29*x^3+9*x^2+45*x+32", "y^2=38*x^6+19*x^5+13*x^4+45*x^3+6*x^2+7*x+38", "y^2=43*x^6+24*x^5+14*x^4+7*x^3+28*x^2+41*x+30", "y^2=54*x^6+36*x^5+46*x^4+46*x^3+59*x^2+46*x+1", "y^2=51*x^6+31*x^5+39*x^4+57*x^3+28*x^2+34*x+23", "y^2=13*x^6+39*x^5+27*x^4+57*x^3+20*x^2+34*x+50", "y^2=37*x^6+7*x^5+50*x^3+40*x^2+29*x+15", "y^2=24*x^6+5*x^5+7*x^4+15*x^3+19*x^2+x+27"], "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": 1, "g": 2, "galois_groups": ["4T3"], "geom_dim1_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_distinct": 1, "geom_dim2_factors": 1, "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": ["4.0.12519696.1"], "geometric_splitting_field": "4.0.12519696.1", "geometric_splitting_polynomials": [[1121, -70, 65, 0, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 18, "is_cyclic": true, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 18, "label": "2.61.au_ih", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["4.0.12519696.1"], "p": 61, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 3, 1, 2], [1, 19, 1, 6], [1, 19, 2, 18]], "poly": [1, -20, 215, -1220, 3721], "poly_str": "1 -20 215 -1220 3721 ", "primitive_models": [], "principal_polarization_count": 18, "q": 61, "real_poly": [1, -20, 93], "simple_distinct": ["2.61.au_ih"], "simple_factors": ["2.61.au_ihA"], "simple_multiplicities": [1], "singular_primes": [], "size": 18, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.12519696.1", "splitting_polynomials": [[1121, -70, 65, 0, 1]], "twist_count": 2, "twists": [["2.61.u_ih", "2.3721.be_hff", 2]], "weak_equivalence_count": 1, "zfv_index": 1, "zfv_index_factorization": [], "zfv_is_bass": true, "zfv_is_maximal": true, "zfv_pic_size": 18, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 15969, "zfv_singular_count": 0, "zfv_singular_primes": []}