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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 (34 matches)

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Label Base field Conductor Isogeny class Weierstrass coefficients
32.1-a3 \(\Q(\sqrt{2}) \) 32.1 32.1-a \( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)
32.1-a4 \(\Q(\sqrt{2}) \) 32.1 32.1-a \( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \)
256.1-a3 \(\Q(\sqrt{2}) \) 256.1 256.1-a \( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a + 3\) , \( 0\bigr] \)
256.1-a4 \(\Q(\sqrt{2}) \) 256.1 256.1-a \( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a - 3\) , \( 0\bigr] \)
1024.1-f3 \(\Q(\sqrt{2}) \) 1024.1 1024.1-f \( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 6\) , \( 0\bigr] \)
1024.1-f4 \(\Q(\sqrt{2}) \) 1024.1 1024.1-f \( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 6\) , \( 0\bigr] \)
1024.1-k3 \(\Q(\sqrt{2}) \) 1024.1 1024.1-k \( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( 0\bigr] \)
1024.1-k4 \(\Q(\sqrt{2}) \) 1024.1 1024.1-k \( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 0\bigr] \)
1568.2-c1 \(\Q(\sqrt{2}) \) 1568.2 1568.2-c \( \bigl[0\) , \( 0\) , \( 0\) , \( -16 a - 13\) , \( 0\bigr] \)
1568.2-c2 \(\Q(\sqrt{2}) \) 1568.2 1568.2-c \( \bigl[0\) , \( 0\) , \( 0\) , \( 16 a + 13\) , \( 0\bigr] \)
1568.2-g1 \(\Q(\sqrt{2}) \) 1568.2 1568.2-g \( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a + 5\) , \( 0\bigr] \)
1568.2-g2 \(\Q(\sqrt{2}) \) 1568.2 1568.2-g \( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 5\) , \( 0\bigr] \)
1568.2-i3 \(\Q(\sqrt{2}) \) 1568.2 1568.2-i \( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 9\) , \( 0\bigr] \)
1568.2-i4 \(\Q(\sqrt{2}) \) 1568.2 1568.2-i \( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 9\) , \( 0\bigr] \)
1568.3-c1 \(\Q(\sqrt{2}) \) 1568.3 1568.3-c \( \bigl[0\) , \( 0\) , \( 0\) , \( 16 a - 13\) , \( 0\bigr] \)
1568.3-c2 \(\Q(\sqrt{2}) \) 1568.3 1568.3-c \( \bigl[0\) , \( 0\) , \( 0\) , \( -16 a + 13\) , \( 0\bigr] \)
1568.3-g1 \(\Q(\sqrt{2}) \) 1568.3 1568.3-g \( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 5\) , \( 0\bigr] \)
1568.3-g2 \(\Q(\sqrt{2}) \) 1568.3 1568.3-g \( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 5\) , \( 0\bigr] \)
1568.3-i3 \(\Q(\sqrt{2}) \) 1568.3 1568.3-i \( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a + 9\) , \( 0\bigr] \)
1568.3-i4 \(\Q(\sqrt{2}) \) 1568.3 1568.3-i \( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 9\) , \( 0\bigr] \)
2592.1-c1 \(\Q(\sqrt{2}) \) 2592.1 2592.1-c \( \bigl[0\) , \( 0\) , \( 0\) , \( -27\) , \( 0\bigr] \)
2592.1-c2 \(\Q(\sqrt{2}) \) 2592.1 2592.1-c \( \bigl[0\) , \( 0\) , \( 0\) , \( 27\) , \( 0\bigr] \)
2592.1-d3 \(\Q(\sqrt{2}) \) 2592.1 2592.1-d \( \bigl[0\) , \( 0\) , \( 0\) , \( 9\) , \( 0\bigr] \)
2592.1-d4 \(\Q(\sqrt{2}) \) 2592.1 2592.1-d \( \bigl[0\) , \( 0\) , \( 0\) , \( -9\) , \( 0\bigr] \)
2592.1-f1 \(\Q(\sqrt{2}) \) 2592.1 2592.1-f \( \bigl[0\) , \( 0\) , \( 0\) , \( -3\) , \( 0\bigr] \)
2592.1-f2 \(\Q(\sqrt{2}) \) 2592.1 2592.1-f \( \bigl[0\) , \( 0\) , \( 0\) , \( 3\) , \( 0\bigr] \)
4096.1-e1 \(\Q(\sqrt{2}) \) 4096.1 4096.1-e \( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a + 2\) , \( 0\bigr] \)
4096.1-e2 \(\Q(\sqrt{2}) \) 4096.1 4096.1-e \( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a - 2\) , \( 0\bigr] \)
4096.1-f1 \(\Q(\sqrt{2}) \) 4096.1 4096.1-f \( \bigl[0\) , \( 0\) , \( 0\) , \( a - 1\) , \( 0\bigr] \)
4096.1-f2 \(\Q(\sqrt{2}) \) 4096.1 4096.1-f \( \bigl[0\) , \( 0\) , \( 0\) , \( -a + 1\) , \( 0\bigr] \)
4096.1-g1 \(\Q(\sqrt{2}) \) 4096.1 4096.1-g \( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a + 2\) , \( 0\bigr] \)
4096.1-g2 \(\Q(\sqrt{2}) \) 4096.1 4096.1-g \( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a - 2\) , \( 0\bigr] \)
4096.1-h1 \(\Q(\sqrt{2}) \) 4096.1 4096.1-h \( \bigl[0\) , \( 0\) , \( 0\) , \( -a - 1\) , \( 0\bigr] \)
4096.1-h2 \(\Q(\sqrt{2}) \) 4096.1 4096.1-h \( \bigl[0\) , \( 0\) , \( 0\) , \( a + 1\) , \( 0\bigr] \)
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