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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 (10 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-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-a3 \(\Q(\zeta_{15})^+\) 25.1 25.1-a \( \bigl[a^{2} - 1\) , \( a - 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -716912 a^{3} - 592951 a^{2} + 1784272 a + 392379\) , \( 454902270 a^{3} + 376245535 a^{2} - 1132174281 a - 248976264\bigr] \)
25.1-a4 \(\Q(\zeta_{15})^+\) 25.1 25.1-a \( \bigl[a^{2} - 1\) , \( a - 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -11484892 a^{3} - 9499051 a^{2} + 28583937 a + 6285889\) , \( 29062760688 a^{3} + 24037545339 a^{2} - 72332262037 a - 15906576101\bigr] \)
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-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-a7 \(\Q(\zeta_{15})^+\) 25.1 25.1-a \( \bigl[a^{3} - 2 a + 1\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a^{2} + a - 1\) , \( 29593 a^{3} + 24472 a^{2} - 73662 a - 16197\) , \( -4979614 a^{3} - 4118597 a^{2} + 12393403 a + 2725431\bigr] \)
25.1-a8 \(\Q(\zeta_{15})^+\) 25.1 25.1-a \( \bigl[a^{3} - 2 a + 1\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a^{2} + a - 1\) , \( -199462 a^{3} - 165053 a^{2} + 496253 a + 109138\) , \( -50977357 a^{3} - 42163431 a^{2} + 126872829 a + 27900618\bigr] \)
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 \( \bigl[0\) , \( a^{3} - 2 a + 1\) , \( a^{2} - 1\) , \( a^{3} + a^{2} - 3 a\) , \( -11017 a^{3} - 9112 a^{2} + 27421 a + 6030\bigr] \)
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