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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 (24 matches)

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Label Base field Conductor Isogeny class Weierstrass coefficients
686.2-a1 \(\Q(\sqrt{2}) \) 686.2 686.2-a \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -44 a - 6\) , \( -66 a - 135\bigr] \)
686.2-a2 \(\Q(\sqrt{2}) \) 686.2 686.2-a \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -304 a - 646\) , \( -4930 a - 6831\bigr] \)
686.2-b1 \(\Q(\sqrt{2}) \) 686.2 686.2-b \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -6 a - 8\) , \( 6 a + 10\bigr] \)
686.2-b2 \(\Q(\sqrt{2}) \) 686.2 686.2-b \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 24 a + 47\) , \( 66 a + 71\bigr] \)
686.2-c1 \(\Q(\sqrt{2}) \) 686.2 686.2-c \( \bigl[1\) , \( -a\) , \( a + 1\) , \( 30 a - 50\) , \( -122 a + 124\bigr] \)
686.2-c2 \(\Q(\sqrt{2}) \) 686.2 686.2-c \( \bigl[1\) , \( -a\) , \( a + 1\) , \( 0\) , \( 0\bigr] \)
686.2-d1 \(\Q(\sqrt{2}) \) 686.2 686.2-d \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 681 a - 1536\) , \( -19223 a + 21843\bigr] \)
686.2-d2 \(\Q(\sqrt{2}) \) 686.2 686.2-d \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( a - 6\) , \( 5 a - 7\bigr] \)
686.2-d3 \(\Q(\sqrt{2}) \) 686.2 686.2-d \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -19 a + 39\) , \( -127 a + 143\bigr] \)
686.2-d4 \(\Q(\sqrt{2}) \) 686.2 686.2-d \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -485 a - 759\) , \( 2705 a + 3591\bigr] \)
686.2-d5 \(\Q(\sqrt{2}) \) 686.2 686.2-d \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 141 a - 321\) , \( -1535 a + 1743\bigr] \)
686.2-d6 \(\Q(\sqrt{2}) \) 686.2 686.2-d \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 2591 a - 4241\) , \( -94831 a + 138943\bigr] \)
686.2-d7 \(\Q(\sqrt{2}) \) 686.2 686.2-d \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -103060 a - 164599\) , \( -23909933 a - 32816619\bigr] \)
686.2-d8 \(\Q(\sqrt{2}) \) 686.2 686.2-d \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 41 a - 96\) , \( 269 a - 307\bigr] \)
686.2-d9 \(\Q(\sqrt{2}) \) 686.2 686.2-d \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 251 a - 2161\) , \( 5169 a - 37057\bigr] \)
686.2-d10 \(\Q(\sqrt{2}) \) 686.2 686.2-d \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 10921 a - 24576\) , \( -1213207 a + 1378643\bigr] \)
686.2-d11 \(\Q(\sqrt{2}) \) 686.2 686.2-d \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -134 a - 376\) , \( 1907 a + 2353\bigr] \)
686.2-d12 \(\Q(\sqrt{2}) \) 686.2 686.2-d \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -37479 a - 93056\) , \( -8696055 a - 9208877\bigr] \)
686.2-e1 \(\Q(\sqrt{2}) \) 686.2 686.2-e \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 478 a - 695\) , \( 6733 a - 9853\bigr] \)
686.2-e2 \(\Q(\sqrt{2}) \) 686.2 686.2-e \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 8 a - 5\) , \( 15 a - 5\bigr] \)
686.2-f1 \(\Q(\sqrt{2}) \) 686.2 686.2-f \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -9 a - 7\) , \( -16 a - 19\bigr] \)
686.2-f2 \(\Q(\sqrt{2}) \) 686.2 686.2-f \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 176 a - 256\) , \( -36 a + 32\bigr] \)
686.2-g1 \(\Q(\sqrt{2}) \) 686.2 686.2-g \( \bigl[1\) , \( a\) , \( a\) , \( -14 a - 39\) , \( 67 a + 51\bigr] \)
686.2-g2 \(\Q(\sqrt{2}) \) 686.2 686.2-g \( \bigl[1\) , \( a\) , \( a\) , \( 36 a + 216\) , \( 64 a + 756\bigr] \)
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