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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
31.4-a1 \(\Q(\zeta_{15})^+\) 31.4 31.4-a \( \bigl[a^{2} - 1\) , \( -a^{3} + 3 a - 1\) , \( a^{3} - 2 a\) , \( -71 a^{3} + 341 a^{2} + 296 a - 1252\) , \( -1813 a^{3} + 4283 a^{2} + 7065 a - 16149\bigr] \)
31.4-a2 \(\Q(\zeta_{15})^+\) 31.4 31.4-a \( \bigl[a^{2} - 1\) , \( -a^{3} + 3 a - 1\) , \( a^{3} - 2 a\) , \( -341 a^{3} + 156 a^{2} + 1091 a - 1022\) , \( 4485 a^{3} - 2644 a^{2} - 14997 a + 14364\bigr] \)
31.4-a3 \(\Q(\zeta_{15})^+\) 31.4 31.4-a \( \bigl[a^{2} - 1\) , \( -a^{3} + 3 a - 1\) , \( a^{3} - 2 a\) , \( -21 a^{3} + 21 a^{2} + 66 a - 102\) , \( 51 a^{3} + 19 a^{2} - 157 a - 1\bigr] \)
31.4-a4 \(\Q(\zeta_{15})^+\) 31.4 31.4-a \( \bigl[a^{2} - 1\) , \( -a^{3} + 3 a - 1\) , \( a^{3} - 2 a\) , \( -6 a^{3} + 21 a^{2} + 21 a - 77\) , \( -21 a^{3} + 61 a^{2} + 84 a - 229\bigr] \)
31.4-a5 \(\Q(\zeta_{15})^+\) 31.4 31.4-a \( \bigl[a^{2} - 1\) , \( -a^{3} + 3 a - 1\) , \( a^{3} - 2 a\) , \( -a^{3} + a^{2} + a - 2\) , \( -a^{3} + a^{2} + 4 a - 6\bigr] \)
31.4-a6 \(\Q(\zeta_{15})^+\) 31.4 31.4-a \( \bigl[a^{2} - 1\) , \( -a^{3} + 3 a - 1\) , \( a^{3} - 2 a\) , \( 59 a^{3} - 114 a^{2} - 239 a + 418\) , \( 45 a^{3} + 134 a^{2} - 121 a - 414\bigr] \)
31.4-b1 \(\Q(\zeta_{15})^+\) 31.4 31.4-b \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 0\) , \( 20 a^{3} + 20 a^{2} - 55 a - 94\) , \( -92 a^{3} - 99 a^{2} + 265 a + 402\bigr] \)
31.4-b2 \(\Q(\zeta_{15})^+\) 31.4 31.4-b \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 0\) , \( -4\) , \( -4 a^{3} - 4 a^{2} + 11 a + 10\bigr] \)
31.4-b3 \(\Q(\zeta_{15})^+\) 31.4 31.4-b \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 0\) , \( 1\) , \( 0\bigr] \)
31.4-b4 \(\Q(\zeta_{15})^+\) 31.4 31.4-b \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 0\) , \( -20 a^{3} - 20 a^{2} + 55 a + 6\) , \( -92 a^{3} - 85 a^{2} + 241 a + 58\bigr] \)
31.4-b5 \(\Q(\zeta_{15})^+\) 31.4 31.4-b \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 0\) , \( -20 a^{3} - 25 a^{2} + 45 a + 41\) , \( -93 a^{3} - 101 a^{2} + 280 a + 46\bigr] \)
31.4-b6 \(\Q(\zeta_{15})^+\) 31.4 31.4-b \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 0\) , \( -340 a^{3} - 335 a^{2} + 945 a + 131\) , \( -5083 a^{3} - 4753 a^{2} + 13402 a + 2742\bigr] \)
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