data: - - Ciso: 69828bb Clabel: 69828bb2 Cnumber: 2 abc_quality: 0.8915933416516306 absD: 33796752 adelic_genus: 0 adelic_index: 16 adelic_level: 1518 ainvs: - 0 - 1 - 0 - -1418 - 20085 analytic_rank: 1 bad_primes: - 2 - 3 - 11 - 23 class_deg: 3 class_size: 2 cm: 0 conductor: 69828 degree: 31104 elladic_images: - 3.4.0.1 faltings_height: __RealLiteral__: 0 data: '0.47533020246230773264782797724' prec: 103 faltings_index: 1 faltings_ratio: 3 id: 461926 iso_nlabel: 25 isogeny_degrees: - 1 - 3 jinv: - 37280608000 - 3993 lmfdb_iso: 69828.z lmfdb_label: 69828.z1 lmfdb_number: 1 manin_constant: 1 min_quad_twist_ainvs: - 0 - 1 - 0 - -1418 - 20085 min_quad_twist_disc: 1 modell_images: - 3B modm_images: - 3.4.0.a.1 - 66.8.0.b.1 - 69.8.0-3.a.1.1 - 1518.16.0.? nonmax_primes: - 3 nonmax_rad: 3 num_bad_primes: 4 num_int_pts: 2 optimality: 0 potential_good_reduction: false rank: 1 regulator: __RealLiteral__: 0 data: '1.6936130851693906885590356683' prec: 100 semistable: false sha: 1 sha_primes: [] signD: 1 stable_faltings_height: __RealLiteral__: 0 data: '-0.27830122704586565229237486855' prec: 107 szpiro_ratio: 2.9931812620485614 torsion: 1 torsion_primes: [] torsion_structure: [] - - anlist: - 0 - 1 - 0 - 1 - 0 - 0 - 0 - 4 - 0 - 1 - 0 - 1 - 0 - 2 - 0 - 0 - 0 - 3 - 0 - -2 - 0 aplist: - 0 - 1 - 0 - 4 - 1 - 2 - 3 - -2 - 0 - 3 - -1 - -11 - -6 - 10 - -12 - -12 - 0 - -14 - 4 - -6 - -4 - -8 - 3 - 6 - 1 class_deg: 3 class_size: 2 conductor: 69828 id: 302148 isogeny_matrix: - - 1 - 3 - - 3 - 1 lmfdb_iso: 69828.z trace_hash: 705478925577196017 - - area: __RealLiteral__: 0 data: '0.38648570209508213030425911132' prec: 103 conductor: 69828 gens: - - 21 - 3 - 1 heights: - __RealLiteral__: 0 data: '1.6936130851693906885590356683' prec: 100 id: 461926 lmfdb_label: 69828.z1 ngens: 1 rank_bounds: - 1 - 1 real_period: __RealLiteral__: 0 data: '1.9871728956665025056317299227' prec: 100 sha_an: __RealLiteral__: 0 data: '1.0000000000000000000000000000' prec: 100 special_value: __RealLiteral__: 0 data: '10.096506055784211074417956782193599403' prec: 130 tamagawa_product: 3 torsion_generators: [] xcoord_integral_points: - 21 - - id: 461926 iwdata: '11': - 2 - 0 '13': - 1 - 0 '17': - 1 - 0 '19': - 1 - 0 '2': a '23': a '29': - 1 - 0 '3': - 4 - 0 '31': - 1 - 0 '37': - 1 - 0 '41': - 1 - 0 '43': - 1 - 0 '47': - 1 - 0 '5': - 3 - 1 - 0 '7': - 1 - 0 iwp0: 0 lmfdb_label: 69828.z1 - - degree: 2 field: - -17 - -1 - 1 id: 3320712 lmfdb_label: 69828.z1 torsion: - 3 - degree: 3 field: - -75 - -38 - -1 - 1 id: 3320713 lmfdb_label: 69828.z1 torsion: - 2 - degree: 6 field: - -159 - -141 - 229 - 8 - -36 - -1 - 1 id: 3320716 lmfdb_label: 69828.z1 torsion: - 6 - degree: 6 field: - 67 - -423 - 375 - 95 - -45 - -3 - 1 id: 3320714 lmfdb_label: 69828.z1 torsion: - 2 - 2 - degree: 6 field: - 828 - 0 - 0 - 0 - 0 - 0 - 1 id: 3320715 lmfdb_label: 69828.z1 torsion: - 3 - degree: 12 field: - -891 - 6237 - 1398 - -19920 - 9442 - 11000 - -6632 - -1913 - 1301 - 73 - -68 - -1 - 1 id: 3320719 lmfdb_label: 69828.z1 torsion: - 2 - 6 - degree: 12 field: - 157113 - 0 - -312110 - 0 - -198375 - 0 - -13570 - 0 - -1150 - 0 - 0 - 0 - 1 id: 3320717 lmfdb_label: 69828.z1 torsion: - 4 - degree: 12 field: - 687241 - -4974 - -12399 - 33070 - -12330 - -5094 - 1797 - -126 - 90 - -50 - 21 - -6 - 1 id: 3320718 lmfdb_label: 69828.z1 torsion: - 3 - 3 - degree: 18 field: - -2167109043 - 40013745552 - 76120932591 - 84148725153 - 34185160593 - -2069549415 - -2733873197 - 146795229 - 53962743 - -18777738 - 5327214 - 1062693 - -426053 - -43191 - 11175 - 942 - -141 - -9 - 1 id: 3320720 lmfdb_label: 69828.z1 torsion: - 9 - degree: 18 field: - 4836036987 - -1815100569 - 1941155604 - -278777232 - 209090565 - -92309031 - 45751452 - -13989627 - 5100228 - -1335073 - 544230 - -165771 - 41220 - -7875 - 2313 - -516 - 90 - -9 - 1 id: 3320721 lmfdb_label: 69828.z1 torsion: - 6 - - conductor: 69828 conductor_valuation: 2 discriminant_valuation: 4 id: 1691741 j_denominator_valuation: 0 kodaira_symbol: 4 lmfdb_label: 69828.z1 prime: 2 reduction_type: 0 root_number: -1 tamagawa_number: 1 - conductor: 69828 conductor_valuation: 1 discriminant_valuation: 1 id: 1691742 j_denominator_valuation: 1 kodaira_symbol: 5 lmfdb_label: 69828.z1 prime: 3 reduction_type: 1 root_number: -1 tamagawa_number: 1 - conductor: 69828 conductor_valuation: 1 discriminant_valuation: 3 id: 1691743 j_denominator_valuation: 3 kodaira_symbol: 7 lmfdb_label: 69828.z1 prime: 11 reduction_type: 1 root_number: -1 tamagawa_number: 3 - conductor: 69828 conductor_valuation: 2 discriminant_valuation: 2 id: 1691744 j_denominator_valuation: 0 kodaira_symbol: 2 lmfdb_label: 69828.z1 prime: 23 reduction_type: 0 root_number: -1 tamagawa_number: 1 - - adelic_gens: - - 3 - 4 - 8 - 11 - - 4 - 3 - 9 - 7 - - 1 - 0 - 6 - 1 - - 1268 - 255 - 1 - 760 - - 1257 - 2 - 142 - 7 - - 277 - 6 - 831 - 19 - - 1513 - 6 - 1512 - 7 - - 1 - 6 - 0 - 1 adelic_image: 1518.16.0.? conductor: 69828 id: 2126155 lmfdb_label: 69828.z1 prime: 0 - conductor: 69828 elladic_image: 3.4.0.1 id: 291302 lmfdb_label: 69828.z1 modell_image: 3B prime: 3 - - id: 3577861 lmfdb_iso: 69828.z p: 7 prec: 20 unit: 5633310049111443 val: 1 - id: 3577865 lmfdb_iso: 69828.z p: 13 prec: 20 unit: 577620854465468437167 val: 1 - id: 3577867 lmfdb_iso: 69828.z p: 17 prec: 20 unit: 177619617154393308509963 val: 1 - id: 3577868 lmfdb_iso: 69828.z p: 19 prec: 20 unit: 311531121034629425544124 val: 1 - id: 3577864 lmfdb_iso: 69828.z p: 29 prec: 20 unit: 5458675961611448674335928741 val: 1 - id: 3577875 lmfdb_iso: 69828.z p: 31 prec: 20 unit: 4394299806399867614799723459 val: 1 - id: 3577860 lmfdb_iso: 69828.z p: 37 prec: 20 unit: 298706109004452788893331368309 val: 1 - id: 3577862 lmfdb_iso: 69828.z p: 41 prec: 20 unit: 2220238062711952703311618988037 val: 1 - id: 3577863 lmfdb_iso: 69828.z p: 43 prec: 20 unit: 2795872945838978362138867245646 val: 1 - id: 3577866 lmfdb_iso: 69828.z p: 47 prec: 20 unit: 15132063714122029884344665176415 val: 1 - id: 3577869 lmfdb_iso: 69828.z p: 53 prec: 20 unit: 111065694203473616034283147469948 val: 1 - id: 3577874 lmfdb_iso: 69828.z p: 61 prec: 20 unit: 7389180959193868874009893835259173 val: 1 - id: 3577859 lmfdb_iso: 69828.z p: 67 prec: 20 unit: 24748108340943875038446662040588417 val: 1 - id: 3577872 lmfdb_iso: 69828.z p: 71 prec: 20 unit: 104904032025352519103904215915544283 val: 1 - id: 3577870 lmfdb_iso: 69828.z p: 73 prec: 20 unit: 102836638188735031985736878061771757 val: 1 - id: 3577873 lmfdb_iso: 69828.z p: 79 prec: 20 unit: 195183005989630081628544198556787133 val: 1 - id: 3577858 lmfdb_iso: 69828.z p: 83 prec: 20 unit: 1224578148989376112141650551756949691 val: 1 - id: 3577871 lmfdb_iso: 69828.z p: 89 prec: 20 unit: 9415173553531523472762338133296081621 val: 1 - id: 3577857 lmfdb_iso: 69828.z p: 97 prec: 20 unit: 5227316120050622913269509890587024537524 val: -1 label_cols: - lmfdb_label - lmfdb_iso - lmfdb_label - lmfdb_label - lmfdb_label - lmfdb_label - lmfdb_label - lmfdb_iso labels: - 69828.z1 - 69828.z - 69828.z1 - 69828.z1 - 69828.z1 - 69828.z1 - 69828.z1 - 69828.z tables: - ec_curvedata - ec_classdata - ec_mwbsd - ec_iwasawa - ec_torsion_growth - ec_localdata - ec_galrep - ec_padic timestamp: '2024-05-21T22:58:09.317964'