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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 (8 matches)

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Label Base field Conductor Isogeny class Weierstrass coefficients
17.1-a1 4.4.4913.1 17.1 17.1-a \( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{3}{2}\) , \( a^{2} - 2 a - 2\) , \( \frac{1}{2} a^{3} - 2 a - \frac{1}{2}\) , \( -\frac{5}{2} a^{3} + 4 a^{2} + 5 a - \frac{1}{2}\) , \( -2 a^{3} + 6 a^{2} - 3 a - 1\bigr] \)
17.1-a2 4.4.4913.1 17.1 17.1-a \( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{1}{2}\) , \( a^{3} - a^{2} - 5 a\) , \( \frac{1}{2} a^{3} - 3 a - \frac{3}{2}\) , \( 26 a^{3} - 13 a^{2} - 161 a - 51\) , \( -134 a^{3} + 69 a^{2} + 839 a + 276\bigr] \)
17.1-a3 4.4.4913.1 17.1 17.1-a \( \bigl[1\) , \( -1\) , \( 1\) , \( -330 a^{3} + 330 a^{2} + 1650 a - 936\) , \( -4996 a^{3} + 4996 a^{2} + 24980 a - 13110\bigr] \)
17.1-a4 4.4.4913.1 17.1 17.1-a \( \bigl[1\) , \( -1\) , \( 1\) , \( 330 a^{3} - 330 a^{2} - 1650 a - 606\) , \( 4996 a^{3} - 4996 a^{2} - 24980 a - 8114\bigr] \)
17.1-a5 4.4.4913.1 17.1 17.1-a \( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \)
17.1-a6 4.4.4913.1 17.1 17.1-a \( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \)
17.1-a7 4.4.4913.1 17.1 17.1-a \( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \)
17.1-a8 4.4.4913.1 17.1 17.1-a \( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 0\bigr] \)
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