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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-a6 \(\Q(\zeta_{15})^+\) 25.1 25.1-a \( \bigl[a^{3} - 2 a\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a + 1\) , \( -35 a^{3} - 31 a^{2} + 85 a + 21\) , \( 110 a^{3} + 91 a^{2} - 273 a - 59\bigr] \)
25.1-a8 \(\Q(\zeta_{15})^+\) 25.1 25.1-a \( \bigl[a^{3} - 2 a + 1\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a^{2} + a - 1\) , \( -199462 a^{3} - 165053 a^{2} + 496253 a + 109138\) , \( -50977357 a^{3} - 42163431 a^{2} + 126872829 a + 27900618\bigr] \)
81.1-a1 \(\Q(\zeta_{15})^+\) 81.1 81.1-a \( \bigl[a^{2} + a - 1\) , \( 0\) , \( a\) , \( -5 a^{3} - 23 a^{2} - 28 a - 6\) , \( 264 a^{3} + 140 a^{2} - 825 a - 176\bigr] \)
81.1-a3 \(\Q(\zeta_{15})^+\) 81.1 81.1-a \( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + 3 a + 1\) , \( 1\) , \( -14 a^{3} + 42 a - 26\) , \( -32 a^{3} + 96 a - 51\bigr] \)
841.10-a1 \(\Q(\zeta_{15})^+\) 841.10 841.10-a \( \bigl[a^{2} - 1\) , \( a^{3} - 4 a\) , \( a^{3} - 3 a + 1\) , \( -4 a^{3} - 15 a^{2} + 18 a - 3\) , \( 17 a^{3} + 44 a^{2} - 78 a - 29\bigr] \)
841.10-a4 \(\Q(\zeta_{15})^+\) 841.10 841.10-a \( \bigl[a^{3} - 3 a\) , \( -a^{3} + 4 a\) , \( a^{3} - 2 a + 1\) , \( -61310 a^{3} - 51000 a^{2} + 151961 a + 33437\) , \( -8814438 a^{3} - 7286362 a^{2} + 21946253 a + 4825929\bigr] \)
841.7-a6 \(\Q(\zeta_{15})^+\) 841.7 841.7-a \( \bigl[a\) , \( a^{3} - 4 a\) , \( a^{3} - 2 a\) , \( -1326257 a^{3} - 1096940 a^{2} + 3300819 a + 725883\) , \( -870443666 a^{3} - 719936036 a^{2} + 2166386079 a + 476409613\bigr] \)
841.7-a8 \(\Q(\zeta_{15})^+\) 841.7 841.7-a \( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} - a^{2} + 2 a + 2\) , \( a^{2} + a - 1\) , \( 28 a^{3} - 85 a^{2} + 44 a + 13\) , \( -229 a^{3} + 748 a^{2} - 502 a - 143\bigr] \)
841.8-a2 \(\Q(\zeta_{15})^+\) 841.8 841.8-a \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{2} + a - 3\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -4944643 a^{3} - 4089726 a^{2} + 12306253 a + 2706273\) , \( 6260338923 a^{3} + 5177869806 a^{2} - 15580916689 a - 3426396906\bigr] \)
841.8-a3 \(\Q(\zeta_{15})^+\) 841.8 841.8-a \( \bigl[a^{3} - 3 a\) , \( -a^{2} + a + 2\) , \( a^{2} + a - 2\) , \( 46 a^{3} + 3 a^{2} - 179 a - 37\) , \( 315 a^{3} + 91 a^{2} - 1189 a - 251\bigr] \)
841.9-a3 \(\Q(\zeta_{15})^+\) 841.9 841.9-a \( \bigl[a^{2} - 2\) , \( a^{3} - 3 a - 1\) , \( a^{3} - 3 a + 1\) , \( 3 a^{3} - 4 a^{2} - 24 a - 18\) , \( 9 a^{3} - 14 a^{2} - 72 a - 1\bigr] \)
841.9-a6 \(\Q(\zeta_{15})^+\) 841.9 841.9-a \( \bigl[a^{3} - 2 a\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{2} + a - 2\) , \( -79220 a^{3} - 66357 a^{2} + 195350 a + 43016\) , \( 13008496 a^{3} + 10780866 a^{2} - 32329042 a - 7110931\bigr] \)
961.10-b4 \(\Q(\zeta_{15})^+\) 961.10 961.10-b \( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -34 a^{3} - 41 a^{2} + 90 a + 18\) , \( 123 a^{3} + 135 a^{2} - 322 a - 72\bigr] \)
961.10-b6 \(\Q(\zeta_{15})^+\) 961.10 961.10-b \( \bigl[a^{3} - 2 a\) , \( a^{3} - 2 a\) , \( 1\) , \( -229681 a^{3} - 190239 a^{2} + 571047 a + 125597\) , \( -63266176 a^{3} - 52330761 a^{2} + 157450333 a + 34625138\bigr] \)
961.7-b3 \(\Q(\zeta_{15})^+\) 961.7 961.7-b \( \bigl[a^{2} - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -2 a^{3} - 17 a^{2} + 53 a - 39\) , \( 28 a^{3} - 155 a^{2} + 201 a - 55\bigr] \)
961.7-b6 \(\Q(\zeta_{15})^+\) 961.7 961.7-b \( \bigl[a^{3} - 3 a + 1\) , \( -a^{2} + 3\) , \( 1\) , \( -945799 a^{3} - 782263 a^{2} + 2353930 a + 517653\) , \( 524197265 a^{3} + 433558794 a^{2} - 1304637727 a - 286902673\bigr] \)
961.8-b2 \(\Q(\zeta_{15})^+\) 961.8 961.8-b \( \bigl[a^{2} + a - 2\) , \( -a^{3} + 2 a + 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -70144 a^{3} - 58044 a^{2} + 174511 a + 38379\) , \( -10627479 a^{3} - 8789766 a^{2} + 26450255 a + 5816663\bigr] \)
961.8-b7 \(\Q(\zeta_{15})^+\) 961.8 961.8-b \( \bigl[a + 1\) , \( -a^{3} - a^{2} + 3 a + 1\) , \( a^{2} - 1\) , \( -22 a^{3} - 7 a^{2} + 86 a - 51\) , \( 10 a^{3} + 29 a^{2} + 68 a - 169\bigr] \)
961.9-b2 \(\Q(\zeta_{15})^+\) 961.9 961.9-b \( \bigl[a^{2} - 2\) , \( a^{3} + a^{2} - 2 a - 2\) , \( a^{2} - 2\) , \( -3449313 a^{3} - 2852961 a^{2} + 8584610 a + 1887842\) , \( 3646894359 a^{3} + 3016313673 a^{2} - 9076497964 a - 1996011239\bigr] \)
961.9-b3 \(\Q(\zeta_{15})^+\) 961.9 961.9-b \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{3} - 3 a + 1\) , \( 62 a^{3} + 19 a^{2} - 234 a - 62\) , \( 439 a^{3} + 129 a^{2} - 1605 a - 346\bigr] \)
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