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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 (1-50 of 76 matches)

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Label Base field Conductor Isogeny class Weierstrass coefficients
1024.1-a1 \(\Q(\sqrt{2}) \) 1024.1 1024.1-a \( \bigl[0\) , \( -1\) , \( 0\) , \( 2 a + 2\) , \( -2 a - 2\bigr] \)
1024.1-a2 \(\Q(\sqrt{2}) \) 1024.1 1024.1-a \( \bigl[0\) , \( 1\) , \( 0\) , \( -2 a - 3\) , \( -2 a - 3\bigr] \)
1024.1-a3 \(\Q(\sqrt{2}) \) 1024.1 1024.1-a \( \bigl[0\) , \( 1\) , \( 0\) , \( -12 a - 23\) , \( 32 a + 37\bigr] \)
1024.1-a4 \(\Q(\sqrt{2}) \) 1024.1 1024.1-a \( \bigl[0\) , \( a\) , \( 0\) , \( -24 a + 32\) , \( 32 a - 48\bigr] \)
1024.1-b1 \(\Q(\sqrt{2}) \) 1024.1 1024.1-b \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 10 a - 1\) , \( -7 a + 15\bigr] \)
1024.1-b2 \(\Q(\sqrt{2}) \) 1024.1 1024.1-b \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -1\) , \( -a - 1\bigr] \)
1024.1-b3 \(\Q(\sqrt{2}) \) 1024.1 1024.1-b \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2 a - 2\) , \( 4 a + 6\bigr] \)
1024.1-b4 \(\Q(\sqrt{2}) \) 1024.1 1024.1-b \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -10 a - 21\) , \( -39 a - 61\bigr] \)
1024.1-c1 \(\Q(\sqrt{2}) \) 1024.1 1024.1-c \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2 a - 2\) , \( -4 a + 6\bigr] \)
1024.1-c2 \(\Q(\sqrt{2}) \) 1024.1 1024.1-c \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -1\) , \( a - 1\bigr] \)
1024.1-c3 \(\Q(\sqrt{2}) \) 1024.1 1024.1-c \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 10 a - 21\) , \( 39 a - 61\bigr] \)
1024.1-c4 \(\Q(\sqrt{2}) \) 1024.1 1024.1-c \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -10 a - 1\) , \( 7 a + 15\bigr] \)
1024.1-d1 \(\Q(\sqrt{2}) \) 1024.1 1024.1-d \( \bigl[0\) , \( -1\) , \( 0\) , \( 20 a - 23\) , \( 40 a - 69\bigr] \)
1024.1-d2 \(\Q(\sqrt{2}) \) 1024.1 1024.1-d \( \bigl[0\) , \( 1\) , \( 0\) , \( 20 a - 23\) , \( -40 a + 69\bigr] \)
1024.1-d3 \(\Q(\sqrt{2}) \) 1024.1 1024.1-d \( \bigl[0\) , \( -1\) , \( 0\) , \( -3\) , \( -1\bigr] \)
1024.1-d4 \(\Q(\sqrt{2}) \) 1024.1 1024.1-d \( \bigl[0\) , \( 1\) , \( 0\) , \( -3\) , \( 1\bigr] \)
1024.1-d5 \(\Q(\sqrt{2}) \) 1024.1 1024.1-d \( \bigl[0\) , \( -1\) , \( 0\) , \( -20 a - 23\) , \( -40 a - 69\bigr] \)
1024.1-d6 \(\Q(\sqrt{2}) \) 1024.1 1024.1-d \( \bigl[0\) , \( 1\) , \( 0\) , \( -20 a - 23\) , \( 40 a + 69\bigr] \)
1024.1-e1 \(\Q(\sqrt{2}) \) 1024.1 1024.1-e \( \bigl[0\) , \( a\) , \( 0\) , \( 24 a + 32\) , \( 32 a + 48\bigr] \)
1024.1-e2 \(\Q(\sqrt{2}) \) 1024.1 1024.1-e \( \bigl[0\) , \( -1\) , \( 0\) , \( 2 a - 3\) , \( -2 a + 3\bigr] \)
1024.1-e3 \(\Q(\sqrt{2}) \) 1024.1 1024.1-e \( \bigl[0\) , \( 1\) , \( 0\) , \( -2 a + 2\) , \( -2 a + 2\bigr] \)
1024.1-e4 \(\Q(\sqrt{2}) \) 1024.1 1024.1-e \( \bigl[0\) , \( -1\) , \( 0\) , \( 12 a - 23\) , \( 32 a - 37\bigr] \)
1024.1-f1 \(\Q(\sqrt{2}) \) 1024.1 1024.1-f \( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 66\) , \( 308 a + 616\bigr] \)
1024.1-f2 \(\Q(\sqrt{2}) \) 1024.1 1024.1-f \( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 66\) , \( -308 a - 616\bigr] \)
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-f5 \(\Q(\sqrt{2}) \) 1024.1 1024.1-f \( \bigl[0\) , \( 0\) , \( 0\) , \( -44 a - 66\) , \( -196 a - 280\bigr] \)
1024.1-f6 \(\Q(\sqrt{2}) \) 1024.1 1024.1-f \( \bigl[0\) , \( 0\) , \( 0\) , \( -44 a - 66\) , \( 196 a + 280\bigr] \)
1024.1-f7 \(\Q(\sqrt{2}) \) 1024.1 1024.1-f \( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 66\) , \( -308 a + 616\bigr] \)
1024.1-f8 \(\Q(\sqrt{2}) \) 1024.1 1024.1-f \( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 66\) , \( 308 a - 616\bigr] \)
1024.1-g1 \(\Q(\sqrt{2}) \) 1024.1 1024.1-g \( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( 0\bigr] \)
1024.1-g2 \(\Q(\sqrt{2}) \) 1024.1 1024.1-g \( \bigl[0\) , \( -a\) , \( 0\) , \( 20 a - 44\) , \( 92 a - 144\bigr] \)
1024.1-g3 \(\Q(\sqrt{2}) \) 1024.1 1024.1-g \( \bigl[0\) , \( -a\) , \( 0\) , \( -4\) , \( 4 a\bigr] \)
1024.1-g4 \(\Q(\sqrt{2}) \) 1024.1 1024.1-g \( \bigl[0\) , \( -a\) , \( 0\) , \( -20 a - 44\) , \( 92 a + 144\bigr] \)
1024.1-h1 \(\Q(\sqrt{2}) \) 1024.1 1024.1-h \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2\) , \( a - 2\bigr] \)
1024.1-h2 \(\Q(\sqrt{2}) \) 1024.1 1024.1-h \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -30 a - 53\) , \( 105 a + 141\bigr] \)
1024.1-h3 \(\Q(\sqrt{2}) \) 1024.1 1024.1-h \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -10 a - 13\) , \( -19 a - 27\bigr] \)
1024.1-h4 \(\Q(\sqrt{2}) \) 1024.1 1024.1-h \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 30 a - 53\) , \( -105 a + 141\bigr] \)
1024.1-i1 \(\Q(\sqrt{2}) \) 1024.1 1024.1-i \( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( 0\bigr] \)
1024.1-i2 \(\Q(\sqrt{2}) \) 1024.1 1024.1-i \( \bigl[0\) , \( a\) , \( 0\) , \( 20 a - 44\) , \( -92 a + 144\bigr] \)
1024.1-i3 \(\Q(\sqrt{2}) \) 1024.1 1024.1-i \( \bigl[0\) , \( a\) , \( 0\) , \( -4\) , \( -4 a\bigr] \)
1024.1-i4 \(\Q(\sqrt{2}) \) 1024.1 1024.1-i \( \bigl[0\) , \( a\) , \( 0\) , \( -20 a - 44\) , \( -92 a - 144\bigr] \)
1024.1-j1 \(\Q(\sqrt{2}) \) 1024.1 1024.1-j \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2\) , \( -a + 2\bigr] \)
1024.1-j2 \(\Q(\sqrt{2}) \) 1024.1 1024.1-j \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -30 a - 53\) , \( -105 a - 141\bigr] \)
1024.1-j3 \(\Q(\sqrt{2}) \) 1024.1 1024.1-j \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -10 a - 13\) , \( 19 a + 27\bigr] \)
1024.1-j4 \(\Q(\sqrt{2}) \) 1024.1 1024.1-j \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 30 a - 53\) , \( 105 a - 141\bigr] \)
1024.1-k1 \(\Q(\sqrt{2}) \) 1024.1 1024.1-k \( \bigl[0\) , \( 0\) , \( 0\) , \( 120 a - 182\) , \( 924 a - 1232\bigr] \)
1024.1-k2 \(\Q(\sqrt{2}) \) 1024.1 1024.1-k \( \bigl[0\) , \( 0\) , \( 0\) , \( 120 a - 182\) , \( -924 a + 1232\bigr] \)
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 \( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 0\bigr] \)
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