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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
71.5-a1 6.6.300125.1 71.5 71.5-a \( \bigl[-6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 29 a - 7\) , \( a^{5} - 8 a^{3} - 4 a^{2} + 7 a + 2\) , \( -6 a^{5} + a^{4} + 44 a^{3} + 23 a^{2} - 28 a - 10\) , \( 108 a^{5} - 25 a^{4} - 776 a^{3} - 378 a^{2} + 466 a + 140\) , \( 536 a^{5} - 123 a^{4} - 3847 a^{3} - 1892 a^{2} + 2295 a + 696\bigr] \)
71.5-a2 6.6.300125.1 71.5 71.5-a \( \bigl[-8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 38 a - 12\) , \( -6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 30 a - 6\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 17 a - 6\) , \( 10 a^{5} - 2 a^{4} - 72 a^{3} - 41 a^{2} + 36 a + 12\) , \( 15 a^{5} - 27 a^{4} - 174 a^{3} - 76 a^{2} + 101 a + 30\bigr] \)
71.5-b1 6.6.300125.1 71.5 71.5-b \( \bigl[-a^{5} + 8 a^{3} + 5 a^{2} - 7 a - 2\) , \( -6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 28 a - 8\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 17 a - 5\) , \( 10 a^{5} - 2 a^{4} - 69 a^{3} - 40 a^{2} + 49 a + 14\) , \( 12 a^{5} + 4 a^{4} - 100 a^{3} - 51 a^{2} + 68 a + 20\bigr] \)
71.5-b2 6.6.300125.1 71.5 71.5-b \( \bigl[a^{5} - 7 a^{3} - 5 a^{2} + 2 a + 2\) , \( a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 1\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 17 a - 5\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} + 4 a^{2} - 10 a - 4\) , \( -2 a^{5} + a^{4} + 14 a^{3} + 4 a^{2} - 8 a - 2\bigr] \)
71.5-c1 6.6.300125.1 71.5 71.5-c \( \bigl[-8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 39 a - 12\) , \( -4 a^{5} + a^{4} + 29 a^{3} + 14 a^{2} - 21 a - 6\) , \( 1\) , \( -944 a^{5} + 1869 a^{4} + 4540 a^{3} - 6026 a^{2} + 652 a + 593\) , \( -34009 a^{5} + 72266 a^{4} + 157382 a^{3} - 246003 a^{2} + 35333 a + 30593\bigr] \)
71.5-c2 6.6.300125.1 71.5 71.5-c \( \bigl[-2 a^{5} + a^{4} + 14 a^{3} + 4 a^{2} - 10 a - 1\) , \( -7 a^{5} + a^{4} + 51 a^{3} + 28 a^{2} - 32 a - 13\) , \( -a^{5} + 8 a^{3} + 4 a^{2} - 6 a - 1\) , \( 5 a^{5} - 38 a^{3} - 22 a^{2} + 26 a + 9\) , \( -3 a^{5} + a^{4} + 21 a^{3} + 8 a^{2} - 12 a - 4\bigr] \)
71.5-c3 6.6.300125.1 71.5 71.5-c \( \bigl[a^{5} - a^{4} - 6 a^{3} + a^{2} + 3 a\) , \( -4 a^{5} + 30 a^{3} + 19 a^{2} - 18 a - 9\) , \( -6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 29 a - 6\) , \( -36 a^{5} - 3 a^{4} + 278 a^{3} + 176 a^{2} - 156 a - 75\) , \( 1119 a^{5} - 361 a^{4} - 7802 a^{3} - 3654 a^{2} + 4623 a + 1358\bigr] \)
71.5-c4 6.6.300125.1 71.5 71.5-c \( \bigl[-2 a^{5} + 15 a^{3} + 10 a^{2} - 9 a - 5\) , \( a^{5} - 7 a^{3} - 5 a^{2} + a + 3\) , \( a + 1\) , \( 1534 a^{5} - 351 a^{4} - 11009 a^{3} - 5421 a^{2} + 6557 a + 1992\) , \( -18999 a^{5} + 4356 a^{4} + 136350 a^{3} + 67090 a^{2} - 81287 a - 24651\bigr] \)
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