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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.


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Label Base field Conductor Isogeny class Weierstrass coefficients
1.1-a1 \(\Q(\sqrt{5}, \sqrt{7})\) 1.1 1.1-a \( \bigl[0\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{20}{23} a - \frac{45}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( \frac{166}{23} a^{3} + \frac{211}{23} a^{2} - \frac{740}{23} a - \frac{750}{23}\) , \( 38 a^{3} + 64 a^{2} - 179 a - 217\bigr] \)
1.1-a2 \(\Q(\sqrt{5}, \sqrt{7})\) 1.1 1.1-a \( \bigl[0\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( 1\) , \( -\frac{348}{23} a^{3} + \frac{1626}{23} a^{2} + \frac{536}{23} a - \frac{4817}{23}\) , \( -\frac{1502}{23} a^{3} + \frac{9038}{23} a^{2} - \frac{10395}{23} a - \frac{3550}{23}\bigr] \)
1.1-a3 \(\Q(\sqrt{5}, \sqrt{7})\) 1.1 1.1-a \( \bigl[0\) , \( \frac{2}{23} a^{3} - \frac{3}{23} a^{2} - \frac{20}{23} a + \frac{45}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{166}{23} a^{3} + \frac{211}{23} a^{2} - \frac{740}{23} a - \frac{750}{23}\) , \( -\frac{876}{23} a^{3} - \frac{1469}{23} a^{2} + \frac{4160}{23} a + \frac{4831}{23}\bigr] \)
1.1-a4 \(\Q(\sqrt{5}, \sqrt{7})\) 1.1 1.1-a \( \bigl[0\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{20}{23} a - \frac{45}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -\frac{162}{23} a^{3} + \frac{703}{23} a^{2} - \frac{220}{23} a - \frac{1092}{23}\) , \( \frac{1038}{23} a^{3} - \frac{4800}{23} a^{2} + \frac{1649}{23} a + \frac{7738}{23}\bigr] \)
1.1-b1 \(\Q(\sqrt{5}, \sqrt{7})\) 1.1 1.1-b \( \bigl[-\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{81}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{61}{23} a^{3} - \frac{333}{23} a^{2} + \frac{218}{23} a + \frac{579}{23}\) , \( \frac{542}{23} a^{3} - \frac{2837}{23} a^{2} + \frac{1158}{23} a + \frac{4720}{23}\bigr] \)
1.1-b2 \(\Q(\sqrt{5}, \sqrt{7})\) 1.1 1.1-b \( \bigl[-\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{81}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -\frac{73}{23} a^{3} - \frac{132}{23} a^{2} + \frac{385}{23} a + \frac{370}{23}\) , \( -\frac{544}{23} a^{3} - \frac{1208}{23} a^{2} + \frac{2933}{23} a + \frac{3561}{23}\bigr] \)
1.1-b3 \(\Q(\sqrt{5}, \sqrt{7})\) 1.1 1.1-b \( \bigl[-\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( \frac{1}{23} a^{3} - \frac{13}{23} a^{2} - \frac{10}{23} a + \frac{80}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{61}{23} a^{3} - \frac{356}{23} a^{2} + \frac{241}{23} a + \frac{740}{23}\) , \( -\frac{470}{23} a^{3} + \frac{2476}{23} a^{2} - \frac{1027}{23} a - \frac{4204}{23}\bigr] \)
1.1-b4 \(\Q(\sqrt{5}, \sqrt{7})\) 1.1 1.1-b \( \bigl[-\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( \frac{1}{23} a^{3} - \frac{13}{23} a^{2} - \frac{10}{23} a + \frac{80}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -\frac{73}{23} a^{3} - \frac{155}{23} a^{2} + \frac{408}{23} a + \frac{531}{23}\) , \( \frac{468}{23} a^{3} + \frac{1069}{23} a^{2} - \frac{2472}{23} a - \frac{3247}{23}\bigr] \)
1.1-c1 \(\Q(\sqrt{5}, \sqrt{7})\) 1.1 1.1-c \( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{2}{23} a^{3} - \frac{3}{23} a^{2} - \frac{43}{23} a + \frac{22}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{4}{23} a^{3} - \frac{75}{23} a^{2} - \frac{17}{23} a + \frac{159}{23}\) , \( -\frac{30}{23} a^{3} - \frac{24}{23} a^{2} + \frac{70}{23} a + \frac{130}{23}\bigr] \)
1.1-c2 \(\Q(\sqrt{5}, \sqrt{7})\) 1.1 1.1-c \( \bigl[-\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( -1\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( -\frac{540}{23} a^{3} + \frac{810}{23} a^{2} + \frac{11610}{23} a - \frac{22454}{23}\) , \( -\frac{6446}{23} a^{3} + \frac{9669}{23} a^{2} + \frac{138589}{23} a - \frac{267073}{23}\bigr] \)
1.1-c3 \(\Q(\sqrt{5}, \sqrt{7})\) 1.1 1.1-c \( \bigl[-\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( -1\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( \frac{540}{23} a^{3} - \frac{810}{23} a^{2} - \frac{11610}{23} a - \frac{10574}{23}\) , \( \frac{6446}{23} a^{3} - \frac{9669}{23} a^{2} - \frac{138589}{23} a - \frac{125261}{23}\bigr] \)
1.1-c4 \(\Q(\sqrt{5}, \sqrt{7})\) 1.1 1.1-c \( \bigl[-\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( -1\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( \frac{510}{23} a^{3} - \frac{765}{23} a^{2} - \frac{10965}{23} a - \frac{9984}{23}\) , \( \frac{7338}{23} a^{3} - \frac{11007}{23} a^{2} - \frac{157767}{23} a - \frac{142589}{23}\bigr] \)
1.1-c5 \(\Q(\sqrt{5}, \sqrt{7})\) 1.1 1.1-c \( \bigl[1\) , \( -1\) , \( 1\) , \( -\frac{540}{23} a^{3} + \frac{810}{23} a^{2} + \frac{11610}{23} a - \frac{22385}{23}\) , \( \frac{6446}{23} a^{3} - \frac{9669}{23} a^{2} - \frac{138589}{23} a + \frac{267027}{23}\bigr] \)
1.1-c6 \(\Q(\sqrt{5}, \sqrt{7})\) 1.1 1.1-c \( \bigl[1\) , \( -1\) , \( 1\) , \( \frac{540}{23} a^{3} - \frac{810}{23} a^{2} - \frac{11610}{23} a - \frac{10505}{23}\) , \( -\frac{6446}{23} a^{3} + \frac{9669}{23} a^{2} + \frac{138589}{23} a + \frac{125215}{23}\bigr] \)
1.1-c7 \(\Q(\sqrt{5}, \sqrt{7})\) 1.1 1.1-c \( \bigl[1\) , \( -1\) , \( 1\) , \( \frac{510}{23} a^{3} - \frac{765}{23} a^{2} - \frac{10965}{23} a - \frac{9915}{23}\) , \( -\frac{7338}{23} a^{3} + \frac{11007}{23} a^{2} + \frac{157767}{23} a + \frac{142543}{23}\bigr] \)
1.1-c8 \(\Q(\sqrt{5}, \sqrt{7})\) 1.1 1.1-c \( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( \frac{2}{23} a^{3} - \frac{3}{23} a^{2} - \frac{43}{23} a + \frac{22}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( \frac{7}{23} a^{3} - \frac{114}{23} a^{2} - \frac{47}{23} a + \frac{560}{23}\) , \( \frac{105}{23} a^{3} - \frac{261}{23} a^{2} - \frac{268}{23} a + \frac{649}{23}\bigr] \)
16.1-a1 \(\Q(\sqrt{5}, \sqrt{7})\) 16.1 16.1-a \( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{80}{23}\) , \( \frac{5}{23} a^{3} + \frac{4}{23} a^{2} - \frac{96}{23} a - \frac{60}{23}\) , \( 0\) , \( -\frac{62}{23} a^{3} - \frac{45}{23} a^{2} + \frac{91}{23} a + \frac{123}{23}\) , \( \frac{312}{23} a^{3} + \frac{889}{23} a^{2} - \frac{1924}{23} a - \frac{2571}{23}\bigr] \)
16.1-a2 \(\Q(\sqrt{5}, \sqrt{7})\) 16.1 16.1-a \( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( -\frac{3}{23} a^{3} - \frac{7}{23} a^{2} + \frac{76}{23} a + \frac{36}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( -\frac{5}{23} a^{3} + \frac{19}{23} a^{2} + \frac{4}{23} a - \frac{78}{23}\) , \( \frac{30}{23} a^{3} - \frac{22}{23} a^{2} - \frac{392}{23} a - \frac{291}{23}\bigr] \)
16.1-a3 \(\Q(\sqrt{5}, \sqrt{7})\) 16.1 16.1-a \( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{80}{23}\) , \( \frac{5}{23} a^{3} + \frac{4}{23} a^{2} - \frac{96}{23} a - \frac{60}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( -\frac{164}{23} a^{3} + \frac{476}{23} a^{2} + \frac{1847}{23} a - \frac{3874}{23}\) , \( \frac{715}{23} a^{3} - \frac{2211}{23} a^{2} - \frac{8093}{23} a + \frac{19204}{23}\bigr] \)
16.1-a4 \(\Q(\sqrt{5}, \sqrt{7})\) 16.1 16.1-a \( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{80}{23}\) , \( \frac{5}{23} a^{3} + \frac{4}{23} a^{2} - \frac{96}{23} a - \frac{60}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( -\frac{39}{23} a^{3} + \frac{116}{23} a^{2} + \frac{252}{23} a - \frac{199}{23}\) , \( -\frac{10}{23} a^{3} + \frac{107}{23} a^{2} - \frac{245}{23} a - \frac{202}{23}\bigr] \)
16.1-b1 \(\Q(\sqrt{5}, \sqrt{7})\) 16.1 16.1-b \( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( -\frac{5}{23} a^{3} - \frac{4}{23} a^{2} + \frac{96}{23} a + \frac{37}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{80}{23}\) , \( \frac{28}{23} a^{3} - \frac{249}{23} a^{2} + \frac{502}{23} a + \frac{193}{23}\) , \( -\frac{514}{23} a^{3} + \frac{2473}{23} a^{2} + \frac{195}{23} a - \frac{5953}{23}\bigr] \)
16.1-b2 \(\Q(\sqrt{5}, \sqrt{7})\) 16.1 16.1-b \( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( -\frac{5}{23} a^{3} - \frac{4}{23} a^{2} + \frac{96}{23} a + \frac{37}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{80}{23}\) , \( -\frac{7}{23} a^{3} - \frac{24}{23} a^{2} + \frac{162}{23} a + \frac{268}{23}\) , \( -\frac{17}{23} a^{3} + \frac{37}{23} a^{2} + \frac{124}{23} a + \frac{112}{23}\bigr] \)
16.1-b3 \(\Q(\sqrt{5}, \sqrt{7})\) 16.1 16.1-b \( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( -\frac{5}{23} a^{3} - \frac{4}{23} a^{2} + \frac{96}{23} a + \frac{37}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( -\frac{10}{23} a^{3} + \frac{15}{23} a^{2} + \frac{100}{23} a - \frac{41}{23}\) , \( -\frac{1}{23} a^{3} - \frac{10}{23} a^{2} + \frac{33}{23} a + \frac{35}{23}\bigr] \)
16.1-b4 \(\Q(\sqrt{5}, \sqrt{7})\) 16.1 16.1-b \( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( -\frac{5}{23} a^{3} - \frac{4}{23} a^{2} + \frac{96}{23} a + \frac{37}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( 5 a^{3} - 80 a - 82\) , \( -\frac{476}{23} a^{3} - \frac{68}{23} a^{2} + \frac{6922}{23} a + \frac{6655}{23}\bigr] \)
25.1-a1 \(\Q(\sqrt{5}, \sqrt{7})\) 25.1 25.1-a \( \bigl[0\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{11}{23} a^{3} - \frac{5}{23} a^{2} - \frac{156}{23} a + \frac{6}{23}\) , \( -\frac{11}{23} a^{3} + \frac{5}{23} a^{2} + \frac{179}{23} a + \frac{40}{23}\bigr] \)
25.1-b1 \(\Q(\sqrt{5}, \sqrt{7})\) 25.1 25.1-b \( \bigl[0\) , \( 0\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -12 a^{2} + 12 a + 25\) , \( -\frac{582}{23} a^{3} + \frac{873}{23} a^{2} + \frac{967}{23} a - \frac{698}{23}\bigr] \)
25.1-c1 \(\Q(\sqrt{5}, \sqrt{7})\) 25.1 25.1-c \( \bigl[0\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( -\frac{5}{23} a^{3} - \frac{4}{23} a^{2} + \frac{27}{23} a + \frac{106}{23}\) , \( -\frac{3}{23} a^{3} - \frac{7}{23} a^{2} + \frac{7}{23} a - \frac{79}{23}\bigr] \)
25.1-d1 \(\Q(\sqrt{5}, \sqrt{7})\) 25.1 25.1-d \( \bigl[0\) , \( 0\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( \frac{96}{23} a^{3} - \frac{144}{23} a^{2} - \frac{2064}{23} a - \frac{1865}{23}\) , \( -44 a^{3} + 66 a^{2} + 946 a + 853\bigr] \)
25.1-e1 \(\Q(\sqrt{5}, \sqrt{7})\) 25.1 25.1-e \( \bigl[0\) , \( \frac{3}{23} a^{3} - \frac{16}{23} a^{2} - \frac{30}{23} a + \frac{102}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( \frac{11}{23} a^{3} - \frac{5}{23} a^{2} - \frac{156}{23} a + \frac{6}{23}\) , \( \frac{9}{23} a^{3} - \frac{2}{23} a^{2} - \frac{136}{23} a - \frac{200}{23}\bigr] \)
25.1-f1 \(\Q(\sqrt{5}, \sqrt{7})\) 25.1 25.1-f \( \bigl[0\) , \( \frac{1}{23} a^{3} - \frac{13}{23} a^{2} + \frac{13}{23} a + \frac{103}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -\frac{5}{23} a^{3} - \frac{4}{23} a^{2} + \frac{27}{23} a + \frac{106}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} + \frac{36}{23} a - \frac{81}{23}\bigr] \)
29.1-a1 \(\Q(\sqrt{5}, \sqrt{7})\) 29.1 29.1-a \( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{44}{23}\) , \( \frac{1}{23} a^{3} - \frac{13}{23} a^{2} - \frac{10}{23} a + \frac{126}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -\frac{8}{23} a^{3} + \frac{35}{23} a^{2} - \frac{58}{23} a + \frac{257}{23}\) , \( \frac{81}{23} a^{3} - \frac{432}{23} a^{2} + \frac{110}{23} a + \frac{1006}{23}\bigr] \)
29.1-a2 \(\Q(\sqrt{5}, \sqrt{7})\) 29.1 29.1-a \( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -a + 1\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( \frac{54}{23} a^{3} + \frac{103}{23} a^{2} - \frac{425}{23} a - \frac{142}{23}\) , \( \frac{129}{23} a^{3} + \frac{232}{23} a^{2} - \frac{876}{23} a - \frac{605}{23}\bigr] \)
29.1-b1 \(\Q(\sqrt{5}, \sqrt{7})\) 29.1 29.1-b \( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} + \frac{10}{23} a - \frac{80}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{10}{23} a - \frac{58}{23}\) , \( 0\) , \( 5 a^{2} - 3 a - 14\) , \( -\frac{71}{23} a^{3} + \frac{555}{23} a^{2} - \frac{279}{23} a - \frac{1126}{23}\bigr] \)
29.1-b2 \(\Q(\sqrt{5}, \sqrt{7})\) 29.1 29.1-b \( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{4}{23} a^{3} - \frac{6}{23} a^{2} - \frac{63}{23} a + \frac{21}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( \frac{51}{23} a^{3} + \frac{119}{23} a^{2} - \frac{349}{23} a - \frac{382}{23}\) , \( -\frac{157}{23} a^{3} - \frac{305}{23} a^{2} + \frac{926}{23} a + \frac{1079}{23}\bigr] \)
29.2-a1 \(\Q(\sqrt{5}, \sqrt{7})\) 29.2 29.2-a \( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{4}{23} a^{3} - \frac{6}{23} a^{2} - \frac{63}{23} a + \frac{44}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( -\frac{121}{23} a^{3} + \frac{9}{23} a^{2} + \frac{1693}{23} a + \frac{1866}{23}\) , \( -\frac{275}{23} a^{3} - \frac{13}{23} a^{2} + \frac{4015}{23} a + \frac{4082}{23}\bigr] \)
29.2-a2 \(\Q(\sqrt{5}, \sqrt{7})\) 29.2 29.2-a \( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{21}{23}\) , \( -\frac{1}{23} a^{3} - \frac{10}{23} a^{2} + \frac{33}{23} a + \frac{104}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( \frac{17}{23} a^{3} - \frac{106}{23} a^{2} - \frac{147}{23} a + \frac{1153}{23}\) , \( -\frac{160}{23} a^{3} + \frac{424}{23} a^{2} + \frac{1922}{23} a - \frac{3577}{23}\bigr] \)
29.2-b1 \(\Q(\sqrt{5}, \sqrt{7})\) 29.2 29.2-b \( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -a\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{80}{23}\) , \( -\frac{113}{23} a^{3} - \frac{26}{23} a^{2} + \frac{1682}{23} a + \frac{1885}{23}\) , \( \frac{363}{23} a^{3} - \frac{4}{23} a^{2} - \frac{5355}{23} a - \frac{4839}{23}\bigr] \)
29.2-b2 \(\Q(\sqrt{5}, \sqrt{7})\) 29.2 29.2-b \( \bigl[\frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{126}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{20}{23} a + \frac{1}{23}\) , \( \frac{22}{23} a^{3} - \frac{56}{23} a^{2} - \frac{358}{23} a + \frac{863}{23}\) , \( \frac{144}{23} a^{3} - \frac{423}{23} a^{2} - \frac{1785}{23} a + \frac{4137}{23}\bigr] \)
29.3-a1 \(\Q(\sqrt{5}, \sqrt{7})\) 29.3 29.3-a \( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -a + 1\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( \frac{118}{23} a^{3} - \frac{361}{23} a^{2} - \frac{1433}{23} a + \frac{3414}{23}\) , \( \frac{594}{23} a^{3} - \frac{1811}{23} a^{2} - \frac{6998}{23} a + \frac{16677}{23}\bigr] \)
29.3-a2 \(\Q(\sqrt{5}, \sqrt{7})\) 29.3 29.3-a \( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{44}{23}\) , \( \frac{1}{23} a^{3} - \frac{13}{23} a^{2} - \frac{10}{23} a + \frac{126}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( -\frac{13}{23} a^{3} - \frac{61}{23} a^{2} + \frac{245}{23} a + \frac{961}{23}\) , \( \frac{162}{23} a^{3} - \frac{59}{23} a^{2} - \frac{2333}{23} a - \frac{1369}{23}\bigr] \)
29.3-b1 \(\Q(\sqrt{5}, \sqrt{7})\) 29.3 29.3-b \( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{4}{23} a^{3} - \frac{6}{23} a^{2} - \frac{63}{23} a + \frac{21}{23}\) , \( 1\) , \( \frac{122}{23} a^{3} - \frac{367}{23} a^{2} - \frac{1473}{23} a + \frac{3527}{23}\) , \( -\frac{40}{23} a^{3} + \frac{129}{23} a^{2} + \frac{423}{23} a - \frac{1061}{23}\bigr] \)
29.3-b2 \(\Q(\sqrt{5}, \sqrt{7})\) 29.3 29.3-b \( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} + \frac{10}{23} a - \frac{80}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{10}{23} a - \frac{58}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -\frac{21}{23} a^{3} + \frac{43}{23} a^{2} + \frac{417}{23} a + \frac{183}{23}\) , \( -\frac{166}{23} a^{3} + \frac{42}{23} a^{2} + \frac{2626}{23} a + \frac{2337}{23}\bigr] \)
29.4-a1 \(\Q(\sqrt{5}, \sqrt{7})\) 29.4 29.4-a \( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{21}{23}\) , \( -\frac{1}{23} a^{3} - \frac{10}{23} a^{2} + \frac{33}{23} a + \frac{104}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( -\frac{9}{23} a^{3} + \frac{25}{23} a^{2} + \frac{228}{23} a + \frac{292}{23}\) , \( -\frac{83}{23} a^{3} - \frac{186}{23} a^{2} + \frac{554}{23} a + \frac{743}{23}\bigr] \)
29.4-a2 \(\Q(\sqrt{5}, \sqrt{7})\) 29.4 29.4-a \( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{4}{23} a^{3} - \frac{6}{23} a^{2} - \frac{63}{23} a + \frac{44}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{80}{23}\) , \( -\frac{42}{23} a^{3} + \frac{247}{23} a^{2} - \frac{201}{23} a - \frac{370}{23}\) , \( -\frac{250}{23} a^{3} + \frac{1295}{23} a^{2} - \frac{398}{23} a - \frac{2474}{23}\bigr] \)
29.4-b1 \(\Q(\sqrt{5}, \sqrt{7})\) 29.4 29.4-b \( \bigl[\frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{126}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( \frac{14}{23} a^{3} + \frac{48}{23} a^{2} - \frac{209}{23} a - \frac{122}{23}\) , \( \frac{70}{23} a^{3} + \frac{240}{23} a^{2} - \frac{470}{23} a - \frac{725}{23}\bigr] \)
29.4-b2 \(\Q(\sqrt{5}, \sqrt{7})\) 29.4 29.4-b \( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -a\) , \( 1\) , \( -\frac{43}{23} a^{3} + \frac{237}{23} a^{2} - \frac{191}{23} a - \frac{197}{23}\) , \( \frac{24}{23} a^{3} - \frac{105}{23} a^{2} - \frac{79}{23} a + \frac{379}{23}\bigr] \)
36.1-a1 \(\Q(\sqrt{5}, \sqrt{7})\) 36.1 36.1-a \( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{21}{23}\) , \( -\frac{1}{23} a^{3} - \frac{10}{23} a^{2} + \frac{33}{23} a + \frac{104}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} + \frac{10}{23} a - \frac{80}{23}\) , \( -\frac{20}{23} a^{3} - \frac{16}{23} a^{2} + \frac{315}{23} a + \frac{378}{23}\) , \( -\frac{30}{23} a^{3} + \frac{22}{23} a^{2} + \frac{346}{23} a + \frac{291}{23}\bigr] \)
36.1-a2 \(\Q(\sqrt{5}, \sqrt{7})\) 36.1 36.1-a \( \bigl[\frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{20}{23} a + \frac{1}{23}\) , \( -\frac{41}{23} a^{3} + \frac{257}{23} a^{2} - \frac{303}{23} a - \frac{37}{23}\) , \( -\frac{461}{23} a^{3} + \frac{2359}{23} a^{2} - \frac{542}{23} a - \frac{4772}{23}\bigr] \)
36.1-a3 \(\Q(\sqrt{5}, \sqrt{7})\) 36.1 36.1-a \( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{44}{23}\) , \( \frac{3}{23} a^{3} - \frac{16}{23} a^{2} - \frac{30}{23} a + \frac{148}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( -\frac{582}{23} a^{3} + \frac{1655}{23} a^{2} + \frac{7453}{23} a - \frac{16775}{23}\) , \( -\frac{7718}{23} a^{3} + \frac{23629}{23} a^{2} + \frac{90083}{23} a - \frac{215446}{23}\bigr] \)
36.1-a4 \(\Q(\sqrt{5}, \sqrt{7})\) 36.1 36.1-a \( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{21}{23}\) , \( -\frac{1}{23} a^{3} - \frac{10}{23} a^{2} + \frac{33}{23} a + \frac{104}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} + \frac{10}{23} a - \frac{80}{23}\) , \( \frac{10}{23} a^{3} - \frac{176}{23} a^{2} + \frac{475}{23} a + \frac{248}{23}\) , \( -\frac{288}{23} a^{3} + \frac{1398}{23} a^{2} + \frac{74}{23} a - \frac{3559}{23}\bigr] \)
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