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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 (18 matches)

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Label Base field Conductor Isogeny class Weierstrass coefficients
25.1-b1 \(\Q(\zeta_{15})^+\) 25.1 25.1-b \( \bigl[0\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -a + 2\) , \( -a^{2} - a + 3\bigr] \)
25.1-b2 \(\Q(\zeta_{15})^+\) 25.1 25.1-b \( \bigl[0\) , \( a^{3} - 2 a + 1\) , \( a^{2} - 1\) , \( a^{3} + a^{2} - 3 a\) , \( -11017 a^{3} - 9112 a^{2} + 27421 a + 6030\bigr] \)
841.10-b1 \(\Q(\zeta_{15})^+\) 841.10 841.10-b \( \bigl[0\) , \( a^{2} + a - 1\) , \( a^{3} - 3 a\) , \( a^{3} + a^{2} - 2 a\) , \( 216805 a^{3} + 179876 a^{2} - 538381 a - 118433\bigr] \)
841.10-b2 \(\Q(\zeta_{15})^+\) 841.10 841.10-b \( \bigl[0\) , \( -a^{3} - a^{2} + 4 a + 3\) , \( a^{2} + a - 1\) , \( -2 a^{3} - a^{2} + 7 a + 3\) , \( 32 a^{3} + a^{2} - 116 a + 9\bigr] \)
841.7-b1 \(\Q(\zeta_{15})^+\) 841.7 841.7-b \( \bigl[0\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - 2 a + 1\) , \( -2 a^{3} - a^{2} + 7 a + 3\) , \( 18371836 a^{3} + 15195215 a^{2} - 45724292 a - 10055225\bigr] \)
841.7-b2 \(\Q(\zeta_{15})^+\) 841.7 841.7-b \( \bigl[0\) , \( a^{3} - 2 a + 1\) , \( a\) , \( a^{3} + a^{2} - 3 a\) , \( a^{3} - 3 a^{2} - 6 a + 6\bigr] \)
841.8-b1 \(\Q(\zeta_{15})^+\) 841.8 841.8-b \( \bigl[0\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( a^{2} - 2\) , \( -a + 2\) , \( 133196725 a^{3} + 110165536 a^{2} - 331504541 a - 72901094\bigr] \)
841.8-b2 \(\Q(\zeta_{15})^+\) 841.8 841.8-b \( \bigl[0\) , \( a^{2} + a - 1\) , \( a^{3} + a^{2} - 2 a - 2\) , \( a^{3} + a^{2} - 2 a\) , \( -32 a^{3} - 20 a^{2} + 94 a + 20\bigr] \)
841.9-b1 \(\Q(\zeta_{15})^+\) 841.9 841.9-b \( \bigl[0\) , \( -a^{2} - a + 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( a^{3} + a^{2} - 2 a\) , \( -16 a^{3} + 18 a^{2} + 49 a - 60\bigr] \)
841.9-b2 \(\Q(\zeta_{15})^+\) 841.9 841.9-b \( \bigl[0\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 2 a - 2\) , \( -a + 2\) , \( -815183 a^{3} - 674230 a^{2} + 2028854 a + 446165\bigr] \)
961.10-a1 \(\Q(\zeta_{15})^+\) 961.10 961.10-a \( \bigl[0\) , \( -a^{2} - a + 1\) , \( a^{2} + a - 1\) , \( a^{3} + a^{2} - 2 a\) , \( -a^{3} - a^{2} + 2 a\bigr] \)
961.10-a2 \(\Q(\zeta_{15})^+\) 961.10 961.10-a \( \bigl[0\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - 3 a\) , \( -a + 2\) , \( -2365813 a^{3} - 1956743 a^{2} + 5888106 a + 1294853\bigr] \)
961.7-a1 \(\Q(\zeta_{15})^+\) 961.7 961.7-a \( \bigl[0\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -2 a^{3} - a^{2} + 7 a + 3\) , \( -7541548 a^{3} - 6237551 a^{2} + 18769617 a + 4127623\bigr] \)
961.7-a2 \(\Q(\zeta_{15})^+\) 961.7 961.7-a \( \bigl[0\) , \( a^{3} - 2 a + 1\) , \( a^{3} - 3 a + 1\) , \( a^{3} + a^{2} - 3 a\) , \( a^{3} + a^{2} - 2 a - 1\bigr] \)
961.8-a1 \(\Q(\zeta_{15})^+\) 961.8 961.8-a \( \bigl[0\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( a^{3} - 3 a\) , \( -a + 2\) , \( a^{2} - a - 1\bigr] \)
961.8-a2 \(\Q(\zeta_{15})^+\) 961.8 961.8-a \( \bigl[0\) , \( a^{3} - 2 a + 1\) , \( a^{2} + a - 2\) , \( a^{3} + a^{2} - 3 a\) , \( -1139511 a^{3} - 942479 a^{2} + 2836049 a + 623674\bigr] \)
961.9-a1 \(\Q(\zeta_{15})^+\) 961.9 961.9-a \( \bigl[0\) , \( -a^{3} + 2 a - 1\) , \( a^{3} - 3 a + 1\) , \( a^{3} + a^{2} - 3 a\) , \( -a^{2} - a + 3\bigr] \)
961.9-a2 \(\Q(\zeta_{15})^+\) 961.9 961.9-a \( \bigl[0\) , \( -a^{3} - a^{2} + 4 a + 3\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -2 a^{3} - a^{2} + 7 a + 3\) , \( -6908 a^{3} - 5713 a^{2} + 17194 a + 3781\bigr] \)
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