Properties

Base field \(\Q(\zeta_{9})^+\)
Label 3.3.81.1-8.1-a
Conductor 8.1
Rank not recorded

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Base field \(\Q(\zeta_{9})^+\)

Generator \(a\), with minimal polynomial \( x^{3} - 3 x - 1 \); class number \(1\).

Elliptic curves in class 8.1-a over \(\Q(\zeta_{9})^+\)

Isogeny class 8.1-a contains 4 curves linked by isogenies of degrees dividing 21.

Curve label Weierstrass Coefficients
8.1-a1 \( \bigl[a^{2} + a - 1\) , \( -a^{2} + a + 2\) , \( a^{2} - 2\) , \( 13 a^{2} + 2 a - 44\) , \( -22 a^{2} - 3 a + 88\bigr] \)
8.1-a2 \( \bigl[a\) , \( -1\) , \( a^{2} - 1\) , \( 125040 a^{2} - 43189 a - 360486\) , \( 56242078 a^{2} - 19527401 a - 161952511\bigr] \)
8.1-a3 \( \bigl[1\) , \( a^{2} + a - 3\) , \( a^{2} + a - 1\) , \( -a^{2} + 4\) , \( -a - 2\bigr] \)
8.1-a4 \( \bigl[a + 1\) , \( -a\) , \( a^{2} - 1\) , \( 17115 a^{2} - 5866 a - 49431\) , \( 1410206 a^{2} - 489214 a - 4061553\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 7 & 3 & 21 \\ 7 & 1 & 21 & 3 \\ 3 & 21 & 1 & 7 \\ 21 & 3 & 7 & 1 \end{array}\right)\)

Isogeny graph