Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-32.1-a
Conductor 32.1
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 32.1-a over \(\Q(\sqrt{-2}) \)

Isogeny class 32.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
32.1-a1 \( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \)
32.1-a2 \( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)
32.1-a3 \( \bigl[a\) , \( -1\) , \( 0\) , \( -2\) , \( 3\bigr] \)
32.1-a4 \( \bigl[a\) , \( -1\) , \( a\) , \( -1\) , \( 0\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph