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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 (12 matches)

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Label Base field Conductor Isogeny class Weierstrass coefficients
31.2-a1 \(\Q(\zeta_{15})^+\) 31.2 31.2-a \( \bigl[a + 1\) , \( a^{3} - 3 a\) , \( a^{2} - 1\) , \( -15 a^{3} - 85 a^{2} + 385 a - 331\) , \( 187 a^{3} - 1626 a^{2} + 3723 a - 2518\bigr] \)
31.2-a2 \(\Q(\zeta_{15})^+\) 31.2 31.2-a \( \bigl[a + 1\) , \( a^{3} - 3 a\) , \( a^{2} - 1\) , \( 270 a^{3} - 70 a^{2} - 655 a - 231\) , \( -2943 a^{3} + 1542 a^{2} + 6186 a + 1507\bigr] \)
31.2-a3 \(\Q(\zeta_{15})^+\) 31.2 31.2-a \( \bigl[a + 1\) , \( a^{3} - 3 a\) , \( a^{2} - 1\) , \( 15 a^{3} - 5 a^{2} - 25 a - 31\) , \( -47 a^{3} + 4 a^{2} + 161 a - 22\bigr] \)
31.2-a4 \(\Q(\zeta_{15})^+\) 31.2 31.2-a \( \bigl[a + 1\) , \( a^{3} - 3 a\) , \( a^{2} - 1\) , \( -5 a^{2} + 20 a - 21\) , \( -21 a^{2} + 62 a - 44\bigr] \)
31.2-a5 \(\Q(\zeta_{15})^+\) 31.2 31.2-a \( \bigl[a + 1\) , \( a^{3} - 3 a\) , \( a^{2} - 1\) , \( -1\) , \( -a^{2} + 2 a - 1\bigr] \)
31.2-a6 \(\Q(\zeta_{15})^+\) 31.2 31.2-a \( \bigl[a + 1\) , \( a^{3} - 3 a\) , \( a^{2} - 1\) , \( 60 a^{2} - 115 a + 9\) , \( -59 a^{3} - 14 a^{2} + 312 a - 163\bigr] \)
31.2-b1 \(\Q(\zeta_{15})^+\) 31.2 31.2-b \( \bigl[a^{3} - 2 a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( a^{2} - 1\) , \( 416 a^{3} + 76 a^{2} - 1585 a - 348\) , \( 6396 a^{3} + 1587 a^{2} - 23865 a - 5050\bigr] \)
31.2-b2 \(\Q(\zeta_{15})^+\) 31.2 31.2-b \( \bigl[a^{3} - 2 a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( a^{2} - 1\) , \( -24 a^{3} - 4 a^{2} + 90 a - 63\) , \( 49 a^{3} + 26 a^{2} - 250 a + 169\bigr] \)
31.2-b3 \(\Q(\zeta_{15})^+\) 31.2 31.2-b \( \bigl[a^{3} - 2 a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( a^{2} - 1\) , \( 26 a^{3} + 6 a^{2} - 100 a - 23\) , \( 93 a^{3} + 20 a^{2} - 358 a - 75\bigr] \)
31.2-b4 \(\Q(\zeta_{15})^+\) 31.2 31.2-b \( \bigl[a^{3} - 2 a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( a^{2} - 1\) , \( 36 a^{3} + 16 a^{2} - 135 a - 18\) , \( 78 a^{3} - 11 a^{2} - 319 a - 36\bigr] \)
31.2-b5 \(\Q(\zeta_{15})^+\) 31.2 31.2-b \( \bigl[a^{3} - 2 a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( a^{2} - 1\) , \( a^{3} + a^{2} - 5 a - 3\) , \( a^{3} + a^{2} - 6 a - 1\bigr] \)
31.2-b6 \(\Q(\zeta_{15})^+\) 31.2 31.2-b \( \bigl[a^{3} - 2 a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( a^{2} - 1\) , \( a^{3} + a^{2} - 5 a + 2\) , \( a^{3} - 2 a\bigr] \)
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