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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-a2 \(\Q(\zeta_{15})^+\) 25.1 25.1-a \( \bigl[a^{2} + a - 2\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{3} - 2 a + 1\) , \( -45 a^{3} - 39 a^{2} + 113 a + 26\) , \( -258 a^{3} - 214 a^{2} + 641 a + 138\bigr] \)
25.1-a4 \(\Q(\zeta_{15})^+\) 25.1 25.1-a \( \bigl[a^{2} - 1\) , \( a - 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -11484892 a^{3} - 9499051 a^{2} + 28583937 a + 6285889\) , \( 29062760688 a^{3} + 24037545339 a^{2} - 72332262037 a - 15906576101\bigr] \)
81.1-a5 \(\Q(\zeta_{15})^+\) 81.1 81.1-a \( \bigl[1\) , \( -1\) , \( a^{3} - 3 a + 1\) , \( -17 a^{3} + 51 a - 32\) , \( 52 a^{3} - 156 a + 82\bigr] \)
81.1-a8 \(\Q(\zeta_{15})^+\) 81.1 81.1-a \( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a^{2} - 1\) , \( -2561 a^{3} - 2096 a^{2} + 6386 a + 1346\) , \( -98327 a^{3} - 81248 a^{2} + 244768 a + 53612\bigr] \)
841.10-a5 \(\Q(\zeta_{15})^+\) 841.10 841.10-a \( \bigl[a^{3} - 2 a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -8 a^{3} - 16 a^{2} + 26 a - 1\) , \( -54 a^{3} - 57 a^{2} + 161 a + 39\bigr] \)
841.10-a8 \(\Q(\zeta_{15})^+\) 841.10 841.10-a \( \bigl[1\) , \( -a^{2} - a + 3\) , \( a^{3} - 2 a + 1\) , \( -3561535 a^{3} - 2945719 a^{2} + 8864042 a + 1949293\) , \( 5022573969 a^{3} + 4154125293 a^{2} - 12500331294 a - 2748945842\bigr] \)
841.7-a2 \(\Q(\zeta_{15})^+\) 841.7 841.7-a \( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( -a^{3} - a^{2} + 3 a + 1\) , \( a^{2} - 1\) , \( -1624209 a^{3} - 1343372 a^{2} + 4042371 a + 888957\) , \( 1544603558 a^{3} + 1277527564 a^{2} - 3844255227 a - 845389548\bigr] \)
841.7-a4 \(\Q(\zeta_{15})^+\) 841.7 841.7-a \( \bigl[a^{3} - 3 a\) , \( -a + 1\) , \( a^{3} - 2 a + 1\) , \( -326 a^{3} - 213 a^{2} + 849 a + 27\) , \( -3635 a^{3} - 3265 a^{2} + 8894 a + 2657\bigr] \)
841.8-a6 \(\Q(\zeta_{15})^+\) 841.8 841.8-a \( \bigl[a\) , \( a^{2} - a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -6055524 a^{3} - 5008513 a^{2} + 15071068 a + 3314280\) , \( -11131060964 a^{3} - 9206399587 a^{2} + 27703314743 a + 6092231498\bigr] \)
841.8-a8 \(\Q(\zeta_{15})^+\) 841.8 841.8-a \( \bigl[1\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{2} + a - 2\) , \( -1125 a^{3} - 897 a^{2} + 2819 a + 527\) , \( 27556 a^{3} + 22887 a^{2} - 68523 a - 15332\bigr] \)
841.9-a2 \(\Q(\zeta_{15})^+\) 841.9 841.9-a \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 2 a - 2\) , \( a^{2} - 2\) , \( -4656162 a^{3} - 3851083 a^{2} + 11588363 a + 2548394\) , \( -7511798086 a^{3} - 6212939993 a^{2} + 18695586113 a + 4111343335\bigr] \)
841.9-a7 \(\Q(\zeta_{15})^+\) 841.9 841.9-a \( \bigl[a + 1\) , \( a^{2} - 3\) , \( a^{3} - 3 a\) , \( -4 a^{3} - 7 a^{2} - 2 a - 16\) , \( 10 a^{3} + 27 a^{2} + 14 a - 12\bigr] \)
961.10-b2 \(\Q(\zeta_{15})^+\) 961.10 961.10-b \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} - 3\) , \( a + 1\) , \( -13246251 a^{3} - 10955859 a^{2} + 32967653 a + 7249914\) , \( 36003341430 a^{3} + 29778036624 a^{2} - 89606185527 a - 19705281836\bigr] \)
961.10-b8 \(\Q(\zeta_{15})^+\) 961.10 961.10-b \( \bigl[a + 1\) , \( -a^{3} + 4 a\) , \( a^{3} - 2 a\) , \( -47 a^{3} - 48 a^{2} + 125 a + 24\) , \( -314 a^{3} - 286 a^{2} + 788 a + 178\bigr] \)
961.7-b1 \(\Q(\zeta_{15})^+\) 961.7 961.7-b \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{2} + a - 2\) , \( -742 a^{3} + 466 a^{2} + 2513 a - 2417\) , \( 13104 a^{3} - 11905 a^{2} - 46670 a + 52371\bigr] \)
961.7-b8 \(\Q(\zeta_{15})^+\) 961.7 961.7-b \( \bigl[1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( 1\) , \( -1158278 a^{3} - 958000 a^{2} + 2882755 a + 633942\) , \( -931622486 a^{3} - 770536492 a^{2} + 2318649718 a + 509893883\bigr] \)
961.8-b3 \(\Q(\zeta_{15})^+\) 961.8 961.8-b \( \bigl[a^{2} + a - 1\) , \( -a^{2} - a + 1\) , \( a^{3} + a^{2} - 2 a - 2\) , \( -30 a^{3} - 5 a^{2} + 107 a - 63\) , \( -10 a^{3} - 73 a^{2} - 69 a + 248\bigr] \)
961.8-b6 \(\Q(\zeta_{15})^+\) 961.8 961.8-b \( \bigl[a^{3} - 2 a\) , \( a^{2} + a - 2\) , \( a^{2} + a - 1\) , \( -4038928 a^{3} - 3340559 a^{2} + 10052203 a + 2210575\) , \( 6056496764 a^{3} + 5009273452 a^{2} - 15073589041 a - 3314830541\bigr] \)
961.9-b5 \(\Q(\zeta_{15})^+\) 961.9 961.9-b \( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( -a + 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -917 a^{3} - 463 a^{2} + 2463 a - 272\) , \( 16332 a^{3} + 10420 a^{2} - 42556 a - 853\bigr] \)
961.9-b8 \(\Q(\zeta_{15})^+\) 961.9 961.9-b \( \bigl[a + 1\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( 1\) , \( -4224272 a^{3} - 3493908 a^{2} + 10513374 a + 2311997\) , \( -6487761039 a^{3} - 5365968522 a^{2} + 16146931708 a + 3550869173\bigr] \)
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