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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 (10 matches)

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Label Base field Conductor Isogeny class Weierstrass coefficients
41.4-a1 6.6.703493.1 41.4 41.4-a \( \bigl[a\) , \( -a^{5} + 6 a^{3} + a^{2} - 6 a - 4\) , \( a^{2} + a - 2\) , \( -2 a^{5} + 13 a^{3} - 9 a^{2} - 11 a + 7\) , \( -4 a^{5} + 3 a^{4} + 10 a^{3} - 3 a^{2} - 7 a - 2\bigr] \)
41.4-a2 6.6.703493.1 41.4 41.4-a \( \bigl[2 a^{5} - a^{4} - 11 a^{3} + 5 a^{2} + 11 a - 1\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 9 a^{2} - 2 a + 3\) , \( a^{5} - a^{4} - 6 a^{3} + 6 a^{2} + 6 a - 4\) , \( 36 a^{5} - 20 a^{4} - 199 a^{3} + 92 a^{2} + 184 a - 31\) , \( -102 a^{5} + 51 a^{4} + 576 a^{3} - 221 a^{2} - 549 a + 38\bigr] \)
41.4-b1 6.6.703493.1 41.4 41.4-b \( \bigl[2 a^{5} - 2 a^{4} - 11 a^{3} + 10 a^{2} + 9 a - 4\) , \( -a^{5} + a^{4} + 5 a^{3} - 4 a^{2} - 3 a - 1\) , \( 3 a^{5} - 2 a^{4} - 17 a^{3} + 10 a^{2} + 17 a - 2\) , \( -6 a^{5} + 5 a^{4} + 34 a^{3} - 23 a^{2} - 33 a + 4\) , \( -6 a^{5} + 3 a^{4} + 36 a^{3} - 15 a^{2} - 43 a + 5\bigr] \)
41.4-b2 6.6.703493.1 41.4 41.4-b \( \bigl[2 a^{5} - 2 a^{4} - 11 a^{3} + 10 a^{2} + 9 a - 4\) , \( -a^{5} + a^{4} + 5 a^{3} - 4 a^{2} - 3 a - 1\) , \( 3 a^{5} - 2 a^{4} - 17 a^{3} + 10 a^{2} + 17 a - 2\) , \( 19 a^{5} - 10 a^{4} - 106 a^{3} + 47 a^{2} + 92 a - 16\) , \( 55 a^{5} - 29 a^{4} - 312 a^{3} + 137 a^{2} + 286 a - 40\bigr] \)
41.4-c1 6.6.703493.1 41.4 41.4-c \( \bigl[a^{5} - 6 a^{3} + a^{2} + 8 a\) , \( -2 a^{5} + 2 a^{4} + 11 a^{3} - 10 a^{2} - 10 a + 4\) , \( a + 1\) , \( 5 a^{5} - a^{4} - 27 a^{3} + 8 a^{2} + 26 a - 1\) , \( -a^{5} + 4 a^{4} + 10 a^{3} - 14 a^{2} - 14 a + 4\bigr] \)
41.4-d1 6.6.703493.1 41.4 41.4-d \( \bigl[2 a^{5} - a^{4} - 12 a^{3} + 6 a^{2} + 13 a - 2\) , \( -2 a^{5} + 2 a^{4} + 11 a^{3} - 11 a^{2} - 9 a + 5\) , \( a^{5} - 6 a^{3} + 8 a + 2\) , \( -2 a^{5} + 3 a^{4} + 10 a^{3} - 16 a^{2} - 7 a + 14\) , \( -6 a^{5} + 16 a^{4} + 27 a^{3} - 92 a^{2} - 3 a + 86\bigr] \)
41.4-e1 6.6.703493.1 41.4 41.4-e \( \bigl[2 a^{5} - a^{4} - 11 a^{3} + 6 a^{2} + 10 a - 3\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 10 a^{2} - a + 6\) , \( a^{5} - 6 a^{3} + a^{2} + 7 a - 1\) , \( 78 a^{5} - 247 a^{4} + 122 a^{3} + 129 a^{2} - 104 a + 23\) , \( 2279 a^{5} - 9254 a^{4} + 8032 a^{3} + 6740 a^{2} - 9382 a + 993\bigr] \)
41.4-e2 6.6.703493.1 41.4 41.4-e \( \bigl[2 a^{5} - a^{4} - 12 a^{3} + 5 a^{2} + 14 a - 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 7 a + 4\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 11 a^{2} + 9 a - 5\) , \( -30 a^{5} + 3 a^{4} + 169 a^{3} - 71 a^{2} - 156 a + 28\) , \( -115 a^{5} - 28 a^{4} + 635 a^{3} - 157 a^{2} - 561 a + 63\bigr] \)
41.4-e3 6.6.703493.1 41.4 41.4-e \( \bigl[2 a^{5} - a^{4} - 12 a^{3} + 5 a^{2} + 14 a - 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 7 a + 4\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 11 a^{2} + 9 a - 5\) , \( -5 a^{5} - 2 a^{4} + 29 a^{3} - a^{2} - 31 a - 2\) , \( -10 a^{5} - 2 a^{4} + 55 a^{3} - 13 a^{2} - 49 a + 5\bigr] \)
41.4-e4 6.6.703493.1 41.4 41.4-e \( \bigl[2 a^{5} - a^{4} - 12 a^{3} + 5 a^{2} + 14 a - 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 7 a + 4\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 11 a^{2} + 9 a - 5\) , \( -5 a^{5} + 3 a^{4} + 29 a^{3} - 16 a^{2} - 31 a + 8\) , \( -a^{5} + 6 a^{3} - a^{2} - 6 a - 2\bigr] \)
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