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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
31.1-a1 \(\Q(\zeta_{15})^+\) 31.1 31.1-a \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 1\) , \( -427 a^{3} - 156 a^{2} + 1210 a - 328\) , \( 5301 a^{3} + 2573 a^{2} - 14446 a + 2048\bigr] \)
31.1-a2 \(\Q(\zeta_{15})^+\) 31.1 31.1-a \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 1\) , \( 113 a^{3} + 114 a^{2} - 280 a - 98\) , \( -a^{3} - 75 a^{2} + 44 a + 78\bigr] \)
31.1-a3 \(\Q(\zeta_{15})^+\) 31.1 31.1-a \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 1\) , \( -37 a^{3} - 21 a^{2} + 105 a - 13\) , \( 2 a^{3} - 25 a^{2} - 17 a + 63\bigr] \)
31.1-a4 \(\Q(\zeta_{15})^+\) 31.1 31.1-a \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 1\) , \( -2 a^{3} - a^{2} + 5 a + 2\) , \( -2 a^{3} - 2 a^{2} + 5 a + 1\bigr] \)
31.1-a5 \(\Q(\zeta_{15})^+\) 31.1 31.1-a \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 1\) , \( -22 a^{3} - 21 a^{2} + 60 a + 12\) , \( -77 a^{3} - 67 a^{2} + 195 a + 43\bigr] \)
31.1-a6 \(\Q(\zeta_{15})^+\) 31.1 31.1-a \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 1\) , \( -327 a^{3} - 341 a^{2} + 895 a + 197\) , \( -4716 a^{3} - 4369 a^{2} + 12267 a + 2711\bigr] \)
31.1-b1 \(\Q(\zeta_{15})^+\) 31.1 31.1-b \( \bigl[a^{2} - 2\) , \( -a^{2} + 1\) , \( 0\) , \( -80 a^{3} + 335 a^{2} + 315 a - 1284\) , \( -2177 a^{3} + 4753 a^{2} + 8378 a - 18117\bigr] \)
31.1-b2 \(\Q(\zeta_{15})^+\) 31.1 31.1-b \( \bigl[a^{2} - 2\) , \( -a^{2} + 1\) , \( 0\) , \( -5 a^{3} + 20 a^{2} + 20 a - 79\) , \( -42 a^{3} + 85 a^{2} + 161 a - 317\bigr] \)
31.1-b3 \(\Q(\zeta_{15})^+\) 31.1 31.1-b \( \bigl[a^{2} - 2\) , \( -a^{2} + 1\) , \( 0\) , \( -10 a^{3} + 25 a^{2} + 45 a - 74\) , \( 9 a^{3} + 101 a^{2} - 28 a - 357\bigr] \)
31.1-b4 \(\Q(\zeta_{15})^+\) 31.1 31.1-b \( \bigl[a^{2} - 2\) , \( -a^{2} + 1\) , \( 0\) , \( 5 a^{3} - 20 a^{2} - 20 a - 9\) , \( -4 a^{3} + 99 a^{2} + 23 a - 5\bigr] \)
31.1-b5 \(\Q(\zeta_{15})^+\) 31.1 31.1-b \( \bigl[a^{2} - 2\) , \( -a^{2} + 1\) , \( 0\) , \( -4\) , \( -a^{3} + 4 a^{2} + 4 a - 7\bigr] \)
31.1-b6 \(\Q(\zeta_{15})^+\) 31.1 31.1-b \( \bigl[a^{2} - 2\) , \( -a^{2} + 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
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