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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 (44 matches)

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Label Base field Conductor Isogeny class Weierstrass coefficients
192.1-a1 \(\Q(\sqrt{21}) \) 192.1 192.1-a \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -31 a - 77\) , \( -157 a - 258\bigr] \)
192.1-a2 \(\Q(\sqrt{21}) \) 192.1 192.1-a \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -36 a - 62\) , \( -155 a - 275\bigr] \)
192.1-b1 \(\Q(\sqrt{21}) \) 192.1 192.1-b \( \bigl[0\) , \( a\) , \( 0\) , \( 36 a - 98\) , \( 155 a - 430\bigr] \)
192.1-b2 \(\Q(\sqrt{21}) \) 192.1 192.1-b \( \bigl[0\) , \( a\) , \( 0\) , \( 31 a - 108\) , \( 157 a - 415\bigr] \)
192.1-c1 \(\Q(\sqrt{21}) \) 192.1 192.1-c \( \bigl[0\) , \( 1\) , \( 0\) , \( -a + 3\) , \( 0\bigr] \)
192.1-c2 \(\Q(\sqrt{21}) \) 192.1 192.1-c \( \bigl[0\) , \( 1\) , \( 0\) , \( 4 a - 12\) , \( 4 a - 12\bigr] \)
192.1-d1 \(\Q(\sqrt{21}) \) 192.1 192.1-d \( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( 4 a + 7\bigr] \)
192.1-d2 \(\Q(\sqrt{21}) \) 192.1 192.1-d \( \bigl[0\) , \( a\) , \( 0\) , \( -45 a - 84\) , \( -135 a - 243\bigr] \)
192.1-d3 \(\Q(\sqrt{21}) \) 192.1 192.1-d \( \bigl[0\) , \( a\) , \( 0\) , \( -25 a - 44\) , \( 81 a + 145\bigr] \)
192.1-d4 \(\Q(\sqrt{21}) \) 192.1 192.1-d \( \bigl[0\) , \( -1\) , \( 0\) , \( -47 a + 128\) , \( 725 a - 2020\bigr] \)
192.1-e1 \(\Q(\sqrt{21}) \) 192.1 192.1-e \( \bigl[0\) , \( -a\) , \( 0\) , \( -78 a + 221\) , \( -4241 a + 11838\bigr] \)
192.1-e2 \(\Q(\sqrt{21}) \) 192.1 192.1-e \( \bigl[0\) , \( -a\) , \( 0\) , \( -3 a + 11\) , \( 4 a - 12\bigr] \)
192.1-e3 \(\Q(\sqrt{21}) \) 192.1 192.1-e \( \bigl[0\) , \( -a\) , \( 0\) , \( 22 a - 59\) , \( 75 a - 210\bigr] \)
192.1-e4 \(\Q(\sqrt{21}) \) 192.1 192.1-e \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -122 a - 217\) , \( 985 a + 1765\bigr] \)
192.1-e5 \(\Q(\sqrt{21}) \) 192.1 192.1-e \( \bigl[0\) , \( -a\) , \( 0\) , \( 322 a - 899\) , \( 4959 a - 13842\bigr] \)
192.1-e6 \(\Q(\sqrt{21}) \) 192.1 192.1-e \( \bigl[0\) , \( -a\) , \( 0\) , \( 1922 a - 5379\) , \( -68449 a + 191102\bigr] \)
192.1-f1 \(\Q(\sqrt{21}) \) 192.1 192.1-f \( \bigl[0\) , \( -a\) , \( 0\) , \( 20 a - 44\) , \( 76 a - 192\bigr] \)
192.1-f2 \(\Q(\sqrt{21}) \) 192.1 192.1-f \( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( 0\bigr] \)
192.1-f3 \(\Q(\sqrt{21}) \) 192.1 192.1-f \( \bigl[0\) , \( -a\) , \( 0\) , \( -4\) , \( 4 a\bigr] \)
192.1-f4 \(\Q(\sqrt{21}) \) 192.1 192.1-f \( \bigl[0\) , \( -a\) , \( 0\) , \( -20 a - 44\) , \( 108 a + 192\bigr] \)
192.1-g1 \(\Q(\sqrt{21}) \) 192.1 192.1-g \( \bigl[0\) , \( 1\) , \( 0\) , \( a + 2\) , \( 0\bigr] \)
192.1-g2 \(\Q(\sqrt{21}) \) 192.1 192.1-g \( \bigl[0\) , \( 1\) , \( 0\) , \( -4 a - 8\) , \( -4 a - 8\bigr] \)
192.1-h1 \(\Q(\sqrt{21}) \) 192.1 192.1-h \( \bigl[0\) , \( a\) , \( 0\) , \( a\) , \( 1\bigr] \)
192.1-h2 \(\Q(\sqrt{21}) \) 192.1 192.1-h \( \bigl[0\) , \( a\) , \( 0\) , \( 6 a - 15\) , \( -15 a + 42\bigr] \)
192.1-i1 \(\Q(\sqrt{21}) \) 192.1 192.1-i \( \bigl[0\) , \( -1\) , \( 0\) , \( 47 a + 81\) , \( -725 a - 1295\bigr] \)
192.1-i2 \(\Q(\sqrt{21}) \) 192.1 192.1-i \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 1\) , \( -4 a + 11\bigr] \)
192.1-i3 \(\Q(\sqrt{21}) \) 192.1 192.1-i \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 25 a - 69\) , \( -81 a + 226\bigr] \)
192.1-i4 \(\Q(\sqrt{21}) \) 192.1 192.1-i \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 45 a - 129\) , \( 135 a - 378\bigr] \)
192.1-j1 \(\Q(\sqrt{21}) \) 192.1 192.1-j \( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( -180\bigr] \)
192.1-j2 \(\Q(\sqrt{21}) \) 192.1 192.1-j \( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
192.1-j3 \(\Q(\sqrt{21}) \) 192.1 192.1-j \( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( 4\bigr] \)
192.1-j4 \(\Q(\sqrt{21}) \) 192.1 192.1-j \( \bigl[0\) , \( -1\) , \( 0\) , \( -24\) , \( -36\bigr] \)
192.1-j5 \(\Q(\sqrt{21}) \) 192.1 192.1-j \( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 220\bigr] \)
192.1-j6 \(\Q(\sqrt{21}) \) 192.1 192.1-j \( \bigl[0\) , \( -1\) , \( 0\) , \( -384\) , \( -2772\bigr] \)
192.1-k1 \(\Q(\sqrt{21}) \) 192.1 192.1-k \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
192.1-k2 \(\Q(\sqrt{21}) \) 192.1 192.1-k \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 20 a - 64\) , \( -108 a + 300\bigr] \)
192.1-k3 \(\Q(\sqrt{21}) \) 192.1 192.1-k \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4\) , \( -4 a + 4\bigr] \)
192.1-k4 \(\Q(\sqrt{21}) \) 192.1 192.1-k \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -20 a - 24\) , \( -76 a - 116\bigr] \)
192.1-l1 \(\Q(\sqrt{21}) \) 192.1 192.1-l \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -a + 1\) , \( 1\bigr] \)
192.1-l2 \(\Q(\sqrt{21}) \) 192.1 192.1-l \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -6 a - 9\) , \( 15 a + 27\bigr] \)
192.1-m1 \(\Q(\sqrt{21}) \) 192.1 192.1-m \( \bigl[0\) , \( 1\) , \( 0\) , \( a - 5\) , \( -48 a - 81\bigr] \)
192.1-m2 \(\Q(\sqrt{21}) \) 192.1 192.1-m \( \bigl[0\) , \( 1\) , \( 0\) , \( -119 a - 220\) , \( -1117 a - 1996\bigr] \)
192.1-n1 \(\Q(\sqrt{21}) \) 192.1 192.1-n \( \bigl[0\) , \( 1\) , \( 0\) , \( 119 a - 339\) , \( 1117 a - 3113\bigr] \)
192.1-n2 \(\Q(\sqrt{21}) \) 192.1 192.1-n \( \bigl[0\) , \( 1\) , \( 0\) , \( -a - 4\) , \( 48 a - 129\bigr] \)
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