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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
31.3-a1 \(\Q(\zeta_{15})^+\) 31.3 31.3-a \( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 495 a^{3} + 69 a^{2} - 1642 a - 353\) , \( -7129 a^{3} - 1543 a^{2} + 24030 a + 5034\bigr] \)
31.3-a2 \(\Q(\zeta_{15})^+\) 31.3 31.3-a \( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 410 a^{3} + 84 a^{2} - 1572 a - 328\) , \( 6096 a^{3} + 1625 a^{2} - 22572 a - 4736\bigr] \)
31.3-a3 \(\Q(\zeta_{15})^+\) 31.3 31.3-a \( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 40 a^{3} + 4 a^{2} - 142 a - 28\) , \( -32 a^{3} - 5 a^{2} + 76 a + 16\bigr] \)
31.3-a4 \(\Q(\zeta_{15})^+\) 31.3 31.3-a \( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 25 a^{3} + 4 a^{2} - 97 a - 18\) , \( 82 a^{3} + 20 a^{2} - 308 a - 64\bigr] \)
31.3-a5 \(\Q(\zeta_{15})^+\) 31.3 31.3-a \( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -a^{2} - 2 a + 2\) , \( 2 a^{3} - 8 a - 1\bigr] \)
31.3-a6 \(\Q(\zeta_{15})^+\) 31.3 31.3-a \( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -175 a^{3} - 61 a^{2} + 638 a + 137\) , \( 89 a^{3} + 13 a^{2} - 402 a - 82\bigr] \)
31.3-b1 \(\Q(\zeta_{15})^+\) 31.3 31.3-b \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 5 a^{3} - 75 a^{2} + 320 a - 384\) , \( 330 a^{3} - 1847 a^{2} + 3763 a - 2740\bigr] \)
31.3-b2 \(\Q(\zeta_{15})^+\) 31.3 31.3-b \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 5 a^{2} - 20 a - 64\) , \( -7 a^{3} - 11 a^{2} + 120 a + 219\bigr] \)
31.3-b3 \(\Q(\zeta_{15})^+\) 31.3 31.3-b \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -5 a^{2} + 20 a - 24\) , \( 7 a^{3} - 35 a^{2} + 64 a - 35\bigr] \)
31.3-b4 \(\Q(\zeta_{15})^+\) 31.3 31.3-b \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -4\) , \( -a^{2} + 4 a + 4\bigr] \)
31.3-b5 \(\Q(\zeta_{15})^+\) 31.3 31.3-b \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
31.3-b6 \(\Q(\zeta_{15})^+\) 31.3 31.3-b \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -5 a^{3} - 15 a^{2} + 40 a + 16\) , \( -8 a^{3} + a^{2} + 125 a - 166\bigr] \)
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