Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-256.1-a
Conductor 256.1
Rank \( 1 \)

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 256.1-a over \(\Q(\sqrt{-2}) \)

Isogeny class 256.1-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
256.1-a1 \( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 1\bigr] \)
256.1-a2 \( \bigl[0\) , \( 1\) , \( 0\) , \( -2\) , \( -2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph