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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 (16 matches)

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Label Base field Conductor Isogeny class Weierstrass coefficients
55.2-a1 4.4.5125.1 55.2 55.2-a \( \bigl[a^{3} - 4 a - 4\) , \( -a - 1\) , \( a\) , \( 64 a^{3} - a^{2} - 383 a - 342\) , \( 655 a^{3} + 104 a^{2} - 3702 a - 3363\bigr] \)
55.2-a2 4.4.5125.1 55.2 55.2-a \( \bigl[a^{3} - 4 a - 4\) , \( -a - 1\) , \( a\) , \( -6 a^{3} - a^{2} + 32 a + 28\) , \( 45 a^{3} + 6 a^{2} - 259 a - 235\bigr] \)
55.2-b1 4.4.5125.1 55.2 55.2-b \( \bigl[a^{2} - a - 4\) , \( -a^{3} + 4 a + 3\) , \( a^{2} - a - 3\) , \( a^{3} - a^{2} - a + 1\) , \( a^{3} - 6 a^{2} + 2 a + 11\bigr] \)
55.2-b2 4.4.5125.1 55.2 55.2-b \( \bigl[a^{2} - a - 4\) , \( -a^{3} + 4 a + 3\) , \( a^{2} - a - 3\) , \( 16 a^{3} - 41 a^{2} - 21 a + 46\) , \( 66 a^{3} - 198 a^{2} - 52 a + 280\bigr] \)
55.2-c1 4.4.5125.1 55.2 55.2-c \( \bigl[a^{2} - 3\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( 1\) , \( -32 a^{3} + 63 a^{2} + 97 a - 182\) , \( -141 a^{3} + 286 a^{2} + 415 a - 821\bigr] \)
55.2-c2 4.4.5125.1 55.2 55.2-c \( \bigl[a^{2} - 3\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( 1\) , \( -2 a^{3} + 3 a^{2} + 7 a - 7\) , \( -2 a^{3} + 2 a^{2} + 7 a - 4\bigr] \)
55.2-c3 4.4.5125.1 55.2 55.2-c \( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 4 a - 5\) , \( a\) , \( -155 a^{3} + 482 a^{2} + 395 a - 1557\) , \( -2048 a^{3} + 6363 a^{2} + 5087 a - 19778\bigr] \)
55.2-c4 4.4.5125.1 55.2 55.2-c \( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 4 a - 5\) , \( a\) , \( 10 a^{3} - 28 a^{2} - 25 a + 88\) , \( -134 a^{3} + 427 a^{2} + 330 a - 1341\bigr] \)
55.2-d1 4.4.5125.1 55.2 55.2-d \( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{3} + 2 a^{2} + 4 a - 5\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - 6 a^{2} + a + 19\) , \( -a^{3} + a^{2} + 5 a - 3\bigr] \)
55.2-d2 4.4.5125.1 55.2 55.2-d \( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{3} + 2 a^{2} + 4 a - 5\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 6 a^{3} - 21 a^{2} - 4 a + 34\) , \( 14 a^{3} - 58 a^{2} + 10 a + 113\bigr] \)
55.2-d3 4.4.5125.1 55.2 55.2-d \( \bigl[a\) , \( -a + 1\) , \( a^{3} - a^{2} - 3 a\) , \( 189 a^{3} - 180 a^{2} - 756 a - 392\) , \( 2259 a^{3} - 2017 a^{2} - 9352 a - 4703\bigr] \)
55.2-d4 4.4.5125.1 55.2 55.2-d \( \bigl[a\) , \( -a + 1\) , \( a^{3} - a^{2} - 3 a\) , \( 4 a^{3} - 15 a^{2} - a + 28\) , \( 85 a^{3} - 41 a^{2} - 410 a - 280\bigr] \)
55.2-e1 4.4.5125.1 55.2 55.2-e \( \bigl[a^{2} - 4\) , \( a^{3} - 5 a - 4\) , \( a^{2} - 3\) , \( -22 a^{3} + 47 a^{2} + 69 a - 141\) , \( 67 a^{3} - 189 a^{2} - 181 a + 592\bigr] \)
55.2-e2 4.4.5125.1 55.2 55.2-e \( \bigl[a^{2} - 4\) , \( a^{3} - 5 a - 4\) , \( a^{2} - 3\) , \( -2 a^{3} + 2 a^{2} + 9 a - 1\) , \( 2 a^{3} - 5 a^{2} - 7 a + 13\bigr] \)
55.2-f1 4.4.5125.1 55.2 55.2-f \( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a + 1\) , \( 219 a^{3} - 805 a^{2} + 81 a + 1343\) , \( 3458 a^{3} - 12790 a^{2} + 996 a + 22447\bigr] \)
55.2-f2 4.4.5125.1 55.2 55.2-f \( \bigl[1\) , \( -a^{3} + 4 a + 4\) , \( a^{3} - 5 a - 4\) , \( -8 a^{3} - a^{2} + 32 a + 20\) , \( -10 a^{3} - 9 a^{2} + 41 a + 47\bigr] \)
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