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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 (22 matches)

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Label Base field Conductor Isogeny class Weierstrass coefficients
64.7-a1 3.3.316.1 64.7 64.7-a \( \bigl[a^{2} - 3\) , \( 1\) , \( 0\) , \( -1090739352869 a^{2} + 577346424073 a + 4634704800810\) , \( 3861852626891805689 a^{2} - 2044142625427945364 a - 16409554549208060949\bigr] \)
64.7-a2 3.3.316.1 64.7 64.7-a \( \bigl[a^{2} - 3\) , \( -a^{2} - a + 4\) , \( a^{2} - 3\) , \( 1698582370190 a^{2} - 899087811257 a - 7217515206526\) , \( -1762034893335112832 a^{2} + 932674283807826223 a + 7487133894869004409\bigr] \)
64.7-a3 3.3.316.1 64.7 64.7-a \( \bigl[a^{2} - 3\) , \( -a^{2} - a + 4\) , \( a^{2} - 3\) , \( 111924466010 a^{2} - 59243475582 a - 475582785731\) , \( -24375873611518938 a^{2} + 12902554057702025 a + 103576512715027461\bigr] \)
64.7-a4 3.3.316.1 64.7 64.7-a \( \bigl[a + 1\) , \( a^{2} - a - 2\) , \( a + 1\) , \( 2665494177 a^{2} - 1410890263 a - 11326059360\) , \( 101937460779857 a^{2} - 53957188127012 a - 433146596953681\bigr] \)
64.7-a5 3.3.316.1 64.7 64.7-a \( \bigl[a + 1\) , \( -a^{2} + 2\) , \( a^{2} - 3\) , \( -2894790049560 a^{2} + 1532260369223 a + 12300369748958\) , \( -6521086825648874308 a^{2} + 3451719377275691295 a + 27709014383527172465\bigr] \)
64.7-a6 3.3.316.1 64.7 64.7-a \( \bigl[a + 1\) , \( -a^{2} + 2\) , \( a + 1\) , \( 7908272 a^{2} - 4185996 a - 33603389\) , \( 17708327376 a^{2} - 9373311330 a - 75245171795\bigr] \)
64.7-a7 3.3.316.1 64.7 64.7-a \( \bigl[a + 1\) , \( -a^{2} + 2\) , \( a + 1\) , \( 494267 a^{2} - 261626 a - 2100214\) , \( 276978244 a^{2} - 146609178 a - 1176919487\bigr] \)
64.7-a8 3.3.316.1 64.7 64.7-a \( \bigl[a + 1\) , \( -a^{2} - a + 4\) , \( a + 1\) , \( 25 a^{2} + 40 a - 45\) , \( -3190 a^{2} - 4343 a + 2671\bigr] \)
64.7-b1 3.3.316.1 64.7 64.7-b \( \bigl[a^{2} + a - 2\) , \( -a^{2} + 2\) , \( a^{2} - 3\) , \( a^{2} + a - 1\) , \( 2 a^{2} + 2 a - 3\bigr] \)
64.7-b2 3.3.316.1 64.7 64.7-b \( \bigl[a^{2} + a - 2\) , \( -a^{2} + 2\) , \( a^{2} - 3\) , \( -2 a^{2} + a + 9\) , \( -a^{2} + a + 5\bigr] \)
64.7-c1 3.3.316.1 64.7 64.7-c \( \bigl[a^{2} + a - 2\) , \( a^{2} - a - 2\) , \( a^{2} - 3\) , \( 3 a^{2} + a - 5\) , \( -2 a^{2} - 4 a\bigr] \)
64.7-c2 3.3.316.1 64.7 64.7-c \( \bigl[a^{2} + a - 2\) , \( a - 1\) , \( a + 1\) , \( -71 a^{2} + 42 a + 312\) , \( 7259 a^{2} - 3836 a - 30834\bigr] \)
64.7-d1 3.3.316.1 64.7 64.7-d \( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( 7908273 a^{2} - 4185996 a - 33603392\) , \( -17708327376 a^{2} + 9373311329 a + 75245171793\bigr] \)
64.7-d2 3.3.316.1 64.7 64.7-d \( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( 494268 a^{2} - 261626 a - 2100217\) , \( -276978244 a^{2} + 146609177 a + 1176919485\bigr] \)
64.7-d3 3.3.316.1 64.7 64.7-d \( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a + 1\) , \( -2894790049560 a^{2} + 1532260369223 a + 12300369748958\) , \( 6521086825648874308 a^{2} - 3451719377275691296 a - 27709014383527172467\bigr] \)
64.7-d4 3.3.316.1 64.7 64.7-d \( \bigl[a^{2} - 3\) , \( a^{2} - 3\) , \( 0\) , \( 27 a^{2} + 42 a - 50\) , \( 3216 a^{2} + 4384 a - 2719\bigr] \)
64.7-d5 3.3.316.1 64.7 64.7-d \( \bigl[a^{2} - 3\) , \( -a^{2} + 3\) , \( 0\) , \( 2665494175 a^{2} - 1410890261 a - 11326059353\) , \( -101934795285681 a^{2} + 53955777236750 a + 433135270894324\bigr] \)
64.7-d6 3.3.316.1 64.7 64.7-d \( \bigl[a + 1\) , \( a^{2} - 3\) , \( 0\) , \( 1698582370192 a^{2} - 899087811255 a - 7217515206531\) , \( 1762036591917483023 a^{2} - 932675182895637479 a - 7487141112384210938\bigr] \)
64.7-d7 3.3.316.1 64.7 64.7-d \( \bigl[a + 1\) , \( a^{2} - 3\) , \( 0\) , \( 111924466012 a^{2} - 59243475580 a - 475582785736\) , \( 24375985535984949 a^{2} - 12902613301177606 a - 103576988297813195\bigr] \)
64.7-d8 3.3.316.1 64.7 64.7-d \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -1090739352869 a^{2} + 577346424071 a + 4634704800807\) , \( -3861853717631158558 a^{2} + 2044143202774369436 a + 16409559183912861757\bigr] \)
64.7-e1 3.3.316.1 64.7 64.7-e \( \bigl[a^{2} + a - 2\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( -73 a^{2} + 41 a + 315\) , \( -7157 a^{2} + 3791 a + 30416\bigr] \)
64.7-e2 3.3.316.1 64.7 64.7-e \( \bigl[a^{2} + a - 2\) , \( a\) , \( a^{2} - 3\) , \( 4 a^{2} + 3 a - 7\) , \( 4 a^{2} + 5 a - 4\bigr] \)
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