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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-a5 \(\Q(\zeta_{15})^+\) 25.1 25.1-a \( \bigl[a^{3} - 2 a\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a + 1\) , \( 5 a^{3} + 4 a^{2} - 15 a + 1\) , \( 14 a^{3} + 13 a^{2} - 36 a - 10\bigr] \)
25.1-a7 \(\Q(\zeta_{15})^+\) 25.1 25.1-a \( \bigl[a^{3} - 2 a + 1\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a^{2} + a - 1\) , \( 29593 a^{3} + 24472 a^{2} - 73662 a - 16197\) , \( -4979614 a^{3} - 4118597 a^{2} + 12393403 a + 2725431\bigr] \)
81.1-a2 \(\Q(\zeta_{15})^+\) 81.1 81.1-a \( \bigl[a^{2} + a - 1\) , \( 0\) , \( a\) , \( 10 a^{3} + 7 a^{2} - 28 a - 6\) , \( 30 a^{3} + 23 a^{2} - 78 a - 17\bigr] \)
81.1-a4 \(\Q(\zeta_{15})^+\) 81.1 81.1-a \( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + 3 a + 1\) , \( 1\) , \( a^{3} - 3 a + 4\) , \( -2 a^{3} + 6 a - 3\bigr] \)
841.10-a2 \(\Q(\zeta_{15})^+\) 841.10 841.10-a \( \bigl[a^{2} - 1\) , \( a^{3} - 4 a\) , \( a^{3} - 3 a + 1\) , \( a^{3} - 2 a + 2\) , \( 2 a^{3} + 2 a^{2} - 5 a - 2\bigr] \)
841.10-a3 \(\Q(\zeta_{15})^+\) 841.10 841.10-a \( \bigl[a^{3} - 3 a\) , \( -a^{3} + 4 a\) , \( a^{3} - 2 a + 1\) , \( 9210 a^{3} + 7600 a^{2} - 22959 a - 5048\) , \( -859607 a^{3} - 710927 a^{2} + 2139516 a + 470497\bigr] \)
841.7-a5 \(\Q(\zeta_{15})^+\) 841.7 841.7-a \( \bigl[a\) , \( a^{3} - 4 a\) , \( a^{3} - 2 a\) , \( 196563 a^{3} + 162575 a^{2} - 489211 a - 107582\) , \( -85653870 a^{3} - 70843538 a^{2} + 213177897 a + 46879917\bigr] \)
841.7-a7 \(\Q(\zeta_{15})^+\) 841.7 841.7-a \( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} - a^{2} + 2 a + 2\) , \( a^{2} + a - 1\) , \( 3 a^{3} - 5 a^{2} - a + 3\) , \( -4 a^{3} + 8 a^{2} - 4 a - 1\bigr] \)
841.8-a1 \(\Q(\zeta_{15})^+\) 841.8 841.8-a \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{2} + a - 3\) , \( a^{3} + a^{2} - 2 a - 1\) , \( 732862 a^{3} + 606139 a^{2} - 1823977 a - 401107\) , \( 617507703 a^{3} + 510735017 a^{2} - 1536871501 a - 337973166\bigr] \)
841.8-a4 \(\Q(\zeta_{15})^+\) 841.8 841.8-a \( \bigl[a^{3} - 3 a\) , \( -a^{2} + a + 2\) , \( a^{2} + a - 2\) , \( 6 a^{3} + 3 a^{2} - 19 a - 2\) , \( 3 a^{3} - a^{2} - 16 a - 4\bigr] \)
841.9-a4 \(\Q(\zeta_{15})^+\) 841.9 841.9-a \( \bigl[a^{2} - 2\) , \( a^{3} - 3 a - 1\) , \( a^{3} - 3 a + 1\) , \( 3 a^{3} + a^{2} - 9 a + 2\) , \( -3 a^{3} - 3 a^{2} + 7 a + 3\bigr] \)
841.9-a5 \(\Q(\zeta_{15})^+\) 841.9 841.9-a \( \bigl[a^{3} - 2 a\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{2} + a - 2\) , \( 12100 a^{3} + 9958 a^{2} - 30230 a - 6644\) , \( 1300517 a^{3} + 1076015 a^{2} - 3235972 a - 711648\bigr] \)
961.10-b3 \(\Q(\zeta_{15})^+\) 961.10 961.10-b \( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( a^{3} + a^{2} - 2 a - 1\) , \( 6 a^{3} + 4 a^{2} - 15 a - 2\) , \( 15 a^{3} + 13 a^{2} - 37 a - 9\bigr] \)
961.10-b5 \(\Q(\zeta_{15})^+\) 961.10 961.10-b \( \bigl[a^{3} - 2 a\) , \( a^{3} - 2 a\) , \( 1\) , \( 34159 a^{3} + 28236 a^{2} - 85053 a - 18703\) , \( -6148692 a^{3} - 5085587 a^{2} + 15302918 a + 3365266\bigr] \)
961.7-b4 \(\Q(\zeta_{15})^+\) 961.7 961.7-b \( \bigl[a^{2} - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 3 a^{3} - 2 a^{2} - 7 a + 6\) , \( -a^{2} + 8 a - 9\bigr] \)
961.7-b5 \(\Q(\zeta_{15})^+\) 961.7 961.7-b \( \bigl[a^{3} - 3 a + 1\) , \( -a^{2} + 3\) , \( 1\) , \( 140176 a^{3} + 115937 a^{2} - 348875 a - 76717\) , \( 51582345 a^{3} + 42663288 a^{2} - 128379673 a - 28231951\bigr] \)
961.8-b1 \(\Q(\zeta_{15})^+\) 961.8 961.8-b \( \bigl[a^{2} + a - 2\) , \( -a^{3} + 2 a + 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( 10406 a^{3} + 8606 a^{2} - 25904 a - 5696\) , \( -1039137 a^{3} - 859459 a^{2} + 2586237 a + 568739\bigr] \)
961.8-b8 \(\Q(\zeta_{15})^+\) 961.8 961.8-b \( \bigl[a + 1\) , \( -a^{3} - a^{2} + 3 a + 1\) , \( a^{2} - 1\) , \( 3 a^{3} - 2 a^{2} - 9 a + 9\) , \( -a^{3} + 4 a^{2} + 7 a - 14\bigr] \)
961.9-b1 \(\Q(\zeta_{15})^+\) 961.9 961.9-b \( \bigl[a^{2} - 2\) , \( a^{3} + a^{2} - 2 a - 2\) , \( a^{2} - 2\) , \( 511247 a^{3} + 422844 a^{2} - 1272415 a - 279818\) , \( 359892277 a^{3} + 297663641 a^{2} - 895710571 a - 196975569\bigr] \)
961.9-b4 \(\Q(\zeta_{15})^+\) 961.9 961.9-b \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{3} - 3 a + 1\) , \( 7 a^{3} + 4 a^{2} - 24 a - 2\) , \( 10 a^{3} + 5 a^{2} - 36 a - 11\bigr] \)
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