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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 (4 matches)

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Label Base field Conductor Isogeny class Weierstrass coefficients
12.2-a1 4.4.18097.1 12.2 12.2-a \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{5}{2} a + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( -8 a^{3} - 10 a^{2} + 28 a + 8\) , \( -46 a^{3} - 75 a^{2} + 133 a + 82\bigr] \)
12.2-a2 4.4.18097.1 12.2 12.2-a \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{3}{2} a - 3\) , \( a^{3} - 4 a\) , \( a^{3} + 2 a^{2} - 14 a - 8\) , \( -7 a^{3} + 36 a + 15\bigr] \)
12.2-b1 4.4.18097.1 12.2 12.2-b \( \bigl[1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( 0\) , \( 6 a^{3} + 3 a^{2} - 38 a - 16\) , \( -14 a^{3} - 5 a^{2} + 92 a + 41\bigr] \)
12.2-b2 4.4.18097.1 12.2 12.2-b \( \bigl[1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{7}{2} a - 1\) , \( a + 1\) , \( -43 a^{3} - 62 a^{2} + 133 a + 49\) , \( \frac{781}{2} a^{3} + \frac{1245}{2} a^{2} - \frac{2273}{2} a - 626\bigr] \)
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