Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-54.1-a
Conductor 54.1
Rank \( 0 \)

Related objects

Learn more about

Base field \(\Q(\sqrt{-2}) \)

Generator \(a\), with minimal polynomial \( x^{2} + 2 \); class number \(1\).

Elliptic curves in class 54.1-a over \(\Q(\sqrt{-2}) \)

Isogeny class 54.1-a contains 4 curves linked by isogenies of degrees dividing 27.

Curve label Weierstrass Coefficients
54.1-a1 \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -a - 1\) , \( -1\bigr] \)
54.1-a2 \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \)
54.1-a3 \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -51 a + 69\) , \( 62 a + 339\bigr] \)
54.1-a4 \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -11 a + 4\) , \( -26\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph