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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
41.1-a1 4.4.5125.1 41.1 41.1-a \( \bigl[0\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - 4\) , \( -6 a^{3} - 2 a^{2} + 25 a + 22\) , \( 8 a^{3} + 7 a^{2} - 30 a - 33\bigr] \)
41.1-b1 4.4.5125.1 41.1 41.1-b \( \bigl[0\) , \( -a^{3} + a^{2} + 4 a\) , \( a^{3} - a^{2} - 3 a\) , \( -9 a^{3} - 7 a^{2} + 37 a + 39\) , \( -31 a^{3} - 23 a^{2} + 126 a + 126\bigr] \)
41.1-c1 4.4.5125.1 41.1 41.1-c \( \bigl[0\) , \( a^{2} - a - 4\) , \( a^{2} - a - 4\) , \( 0\) , \( 0\bigr] \)
41.1-c2 4.4.5125.1 41.1 41.1-c \( \bigl[0\) , \( a^{2} - a - 4\) , \( a^{2} - a - 4\) , \( -10 a^{2} + 10 a\) , \( -31 a^{2} + 31 a + 11\bigr] \)
41.1-d1 4.4.5125.1 41.1 41.1-d \( \bigl[0\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( a^{3} - 4 a - 3\) , \( 144 a^{3} - 153 a^{2} - 559 a - 225\) , \( -1890 a^{3} + 1126 a^{2} + 8698 a + 5670\bigr] \)
41.1-d2 4.4.5125.1 41.1 41.1-d \( \bigl[0\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( a^{3} - 4 a - 3\) , \( 4 a^{3} - 3 a^{2} - 19 a - 5\) , \( 11 a^{3} + a^{2} - 64 a - 61\bigr] \)
41.1-e1 4.4.5125.1 41.1 41.1-e \( \bigl[0\) , \( -a^{2} + 4\) , \( a^{2} - 3\) , \( 6 a^{3} - 20 a^{2} - 3 a + 39\) , \( -9 a^{3} + 32 a^{2} - 5 a - 48\bigr] \)
41.1-f1 4.4.5125.1 41.1 41.1-f \( \bigl[0\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( a^{3} - 4 a - 3\) , \( 9 a^{3} - 34 a^{2} + 4 a + 60\) , \( 30 a^{3} - 115 a^{2} + 15 a + 198\bigr] \)
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