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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 (20 matches)

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Label Base field Conductor Isogeny class Weierstrass coefficients
25.1-a1 \(\Q(\zeta_{15})^+\) 25.1 25.1-a \( \bigl[a^{2} + a - 2\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{3} - 2 a + 1\) , \( -5 a^{3} - 4 a^{2} + 13 a + 6\) , \( -7 a^{3} - 6 a^{2} + 19 a + 4\bigr] \)
25.1-a3 \(\Q(\zeta_{15})^+\) 25.1 25.1-a \( \bigl[a^{2} - 1\) , \( a - 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -716912 a^{3} - 592951 a^{2} + 1784272 a + 392379\) , \( 454902270 a^{3} + 376245535 a^{2} - 1132174281 a - 248976264\bigr] \)
81.1-a6 \(\Q(\zeta_{15})^+\) 81.1 81.1-a \( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a^{2} - 1\) , \( -161 a^{3} - 131 a^{2} + 401 a + 86\) , \( -1640 a^{3} - 1355 a^{2} + 4084 a + 893\bigr] \)
81.1-a7 \(\Q(\zeta_{15})^+\) 81.1 81.1-a \( \bigl[1\) , \( -1\) , \( a^{3} - 3 a + 1\) , \( -2 a^{3} + 6 a - 2\) , \( a^{3} - 3 a + 1\bigr] \)
841.10-a6 \(\Q(\zeta_{15})^+\) 841.10 841.10-a \( \bigl[a^{3} - 2 a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -3 a^{3} - a^{2} + 6 a + 4\) , \( -a^{3} - 4 a^{2} + 6 a + 2\bigr] \)
841.10-a7 \(\Q(\zeta_{15})^+\) 841.10 841.10-a \( \bigl[1\) , \( -a^{2} - a + 3\) , \( a^{3} - 2 a + 1\) , \( -222320 a^{3} - 183879 a^{2} + 553317 a + 121683\) , \( 78789577 a^{3} + 65166142 a^{2} - 196093841 a - 43122964\bigr] \)
841.7-a1 \(\Q(\zeta_{15})^+\) 841.7 841.7-a \( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( -a^{3} - a^{2} + 3 a + 1\) , \( a^{2} - 1\) , \( -101389 a^{3} - 83857 a^{2} + 252341 a + 55492\) , \( 24127676 a^{3} + 19955781 a^{2} - 60049677 a - 13205515\bigr] \)
841.7-a3 \(\Q(\zeta_{15})^+\) 841.7 841.7-a \( \bigl[a^{3} - 3 a\) , \( -a + 1\) , \( a^{3} - 2 a + 1\) , \( -21 a^{3} - 13 a^{2} + 54 a + 2\) , \( -55 a^{3} - 48 a^{2} + 135 a + 37\bigr] \)
841.8-a5 \(\Q(\zeta_{15})^+\) 841.8 841.8-a \( \bigl[a\) , \( a^{2} - a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -378019 a^{3} - 312648 a^{2} + 940838 a + 206900\) , \( -174410939 a^{3} - 144253725 a^{2} + 434079076 a + 95458261\bigr] \)
841.8-a7 \(\Q(\zeta_{15})^+\) 841.8 841.8-a \( \bigl[1\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{2} + a - 2\) , \( -70 a^{3} - 57 a^{2} + 174 a + 37\) , \( 432 a^{3} + 358 a^{2} - 1075 a - 238\bigr] \)
841.9-a1 \(\Q(\zeta_{15})^+\) 841.9 841.9-a \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 2 a - 2\) , \( a^{2} - 2\) , \( -290652 a^{3} - 240393 a^{2} + 723388 a + 159079\) , \( -118023233 a^{3} - 97615947 a^{2} + 293739721 a + 64596254\bigr] \)
841.9-a8 \(\Q(\zeta_{15})^+\) 841.9 841.9-a \( \bigl[a + 1\) , \( a^{2} - 3\) , \( a^{3} - 3 a\) , \( -4 a^{3} - 2 a^{2} + 13 a + 4\) , \( -3 a^{3} - a^{2} + 11 a + 2\bigr] \)
961.10-b1 \(\Q(\zeta_{15})^+\) 961.10 961.10-b \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} - 3\) , \( a + 1\) , \( -826861 a^{3} - 683889 a^{2} + 2057918 a + 452559\) , \( 563758230 a^{3} + 466279311 a^{2} - 1403098227 a - 308555106\bigr] \)
961.10-b7 \(\Q(\zeta_{15})^+\) 961.10 961.10-b \( \bigl[a + 1\) , \( -a^{3} + 4 a\) , \( a^{3} - 2 a\) , \( -7 a^{3} - 3 a^{2} + 20 a + 4\) , \( -9 a^{3} - 9 a^{2} + 27 a + 6\bigr] \)
961.7-b2 \(\Q(\zeta_{15})^+\) 961.7 961.7-b \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{2} + a - 2\) , \( -47 a^{3} + 31 a^{2} + 158 a - 152\) , \( 196 a^{3} - 209 a^{2} - 719 a + 867\bigr] \)
961.7-b7 \(\Q(\zeta_{15})^+\) 961.7 961.7-b \( \bigl[1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( 1\) , \( -72303 a^{3} - 59800 a^{2} + 179950 a + 39572\) , \( -14619624 a^{3} - 12091758 a^{2} + 36385754 a + 8001585\bigr] \)
961.8-b4 \(\Q(\zeta_{15})^+\) 961.8 961.8-b \( \bigl[a^{2} + a - 1\) , \( -a^{2} - a + 1\) , \( a^{3} + a^{2} - 2 a - 2\) , \( -5 a^{3} + 12 a - 3\) , \( -2 a^{3} + 2 a + 2\bigr] \)
961.8-b5 \(\Q(\zeta_{15})^+\) 961.8 961.8-b \( \bigl[a^{3} - 2 a\) , \( a^{2} + a - 2\) , \( a^{2} + a - 1\) , \( -252118 a^{3} - 208524 a^{2} + 627478 a + 137990\) , \( 94587275 a^{3} + 78232276 a^{2} - 235411620 a - 51769332\bigr] \)
961.9-b6 \(\Q(\zeta_{15})^+\) 961.9 961.9-b \( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( -a + 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -57 a^{3} - 28 a^{2} + 153 a - 17\) , \( 195 a^{3} + 119 a^{2} - 512 a + 4\bigr] \)
961.9-b7 \(\Q(\zeta_{15})^+\) 961.9 961.9-b \( \bigl[a + 1\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( 1\) , \( -263712 a^{3} - 218103 a^{2} + 656349 a + 144337\) , \( -101761255 a^{3} - 84165827 a^{2} + 253266390 a + 55695772\bigr] \)
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