{"torsion_structure": [2, 2], "ainvs": "2,-2,-1,1;1,-1,-1,1;1,0,0,0;-30,-72,-24,26;-102,-269,-76,81", "cm": 0, "torsion_gens": ["[[-3,-6,3,1],[0,2,-1,-1],[1,0,0,0]]", "[[-17/4,-3/2,-1/4,1/4],[25/8,-7/2,-3/2,2],[1,0,0,0]]"], "number": 3, "rank": 0, "field_label": "4.4.725.1", "galois_images": ["2Cs"], "conductor_norm": 31, "abs_disc": 725, "iso_nlabel": 0, "rank_bounds": [0, 0], "conductor_ideal": "(w^3-4*w+1)", "base_change": [], "local_data": [{"p": "(w^3-4*w+1)", "cp": 2, "kod": 8, "red": -1, "normp": 31, "rootno": 1, "ord_cond": 1, "ord_disc": 4, "ord_den_j": 4}], "analytic_rank": 0, "minD": "(-25*w^2+20*w+37)", "label": "4.4.725.1-31.1-a3", "jinv": "568721206322809065061/923521,1339721925491697657614/923521,110062957460434799749/923521,-419511683908480280709/923521", "conductor_label": "31.1", "class_deg": 8, "reg": 1, "class_size": 6, "class_label": "4.4.725.1-31.1-a", "iso_label": "a", "degree": 4, "non_min_p": [], "q_curve": false, "short_label": "31.1-a3", "short_class_label": "31.1-a", "isogeny_matrix": [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], "torsion_order": 4, "equation": "{y}^2+\\left(a^{3}-a^{2}-2a+2\\right){x}{y}+{y}={x}^{3}+\\left(a^{3}-a^{2}-a+1\\right){x}^{2}+\\left(26a^{3}-24a^{2}-72a-30\\right){x}+81a^{3}-76a^{2}-269a-102", "gens": [], "ngens": 0, "signature": [4, 0], "trace_hash": 68642452808221503, "heights": [], "isodeg": [1, 2, 4], "omega": {"__RealLiteral__": 0, "data": "32.604239294215157092073484368466738681", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 2, "bad_primes": ["(w^3-4*w+1)"], "Lvalue": {"__RealLiteral__": 0, "data": "0.605445524174481", "prec": 57}, "sha": 4, "torsion_primes": [2], "n_bad_primes": 1, "reducible_primes": [2], "semistable": true, "disc": "(25*w^2-20*w-37)", "normdisc": 923521, "conductor_norm_factors": [31], "nonmax_primes": [2], "nonmax_rad": 2, "root_analytic_conductor": 3.6959643075221122, "cm_type": 0}