Properties

Base field \(\Q(\zeta_{9})^+\)
Label 3.3.81.1-27.1-a
Conductor 27.1
Rank not recorded

Related objects

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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 27.1-a over \(\Q(\zeta_{9})^+\)

Isogeny class 27.1-a contains 4 curves linked by isogenies of degrees dividing 27.

Curve label Weierstrass Coefficients
27.1-a1 \( \bigl[0\) , \( a^{2} + a - 2\) , \( a^{2} - 1\) , \( 280 a^{2} - 89 a - 818\) , \( 2805 a^{2} - 963 a - 8098\bigr] \)
27.1-a2 \( \bigl[0\) , \( a^{2} + a - 2\) , \( a^{2} - 1\) , \( a + 2\) , \( 12 a^{2} - 4 a - 35\bigr] \)
27.1-a3 \( \bigl[0\) , \( a^{2} - 1\) , \( a + 1\) , \( 17 a^{2} - 3 a - 53\) , \( -56 a^{2} + 17 a + 164\bigr] \)
27.1-a4 \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 27 & 9 \\ 3 & 1 & 9 & 3 \\ 27 & 9 & 1 & 3 \\ 9 & 3 & 3 & 1 \end{array}\right)\)

Isogeny graph