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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.


Results (6 matches)

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Label Base field Conductor Isogeny class Weierstrass coefficients
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 \( \bigl[0\) , \( \frac{1}{23} a^{3} - \frac{13}{23} a^{2} + \frac{13}{23} a + \frac{103}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -\frac{5}{23} a^{3} - \frac{4}{23} a^{2} + \frac{27}{23} a + \frac{106}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} + \frac{36}{23} a - \frac{81}{23}\bigr] \)
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